{"id":5567,"date":"2024-10-16T18:59:04","date_gmt":"2024-10-16T18:59:04","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&p=5567"},"modified":"2025-01-27T01:03:06","modified_gmt":"2025-01-27T01:03:06","slug":"glossary-of-terms","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/glossary-of-terms\/","title":{"raw":"Glossary of Terms","rendered":"Glossary of Terms"},"content":{"raw":"
\r\n \t
absolute maximum<\/strong><\/dt>\r\n \t
the greatest value of a function over an interval<\/dd>\r\n<\/dl>\r\n
\r\n \t
absolute minimum<\/strong><\/dt>\r\n \t
the lowest value of a function over an interval<\/dd>\r\n<\/dl>\r\n
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absolute value equation<\/strong><\/dt>\r\n \t
an equation in which the variable appears in absolute value bars, typically with two solutions, one accounting for the positive expression and one for the negative expression<\/dd>\r\n<\/dl>\r\n
\r\n \t
addition method<\/strong><\/dt>\r\n \t
An algebraic technique used to solve systems of linear equations in which the equations are added in a way that eliminates one variable, allowing the resulting equation to be solved for the remaining variable; substitution is then used to solve for the first variable<\/dd>\r\n<\/dl>\r\n
\r\n \t
addition principle<\/strong><\/dt>\r\n \t
if one event can occur in [latex]m[\/latex] ways and a second event with no common outcomes can occur in [latex]n[\/latex] ways, then the first or second event can occur in [latex]m+n[\/latex] ways<\/dd>\r\n<\/dl>\r\n
\r\n \t
algebraic expression<\/strong><\/dt>\r\n \t
constants and variables combined using addition, subtraction, multiplication, and division<\/dd>\r\n<\/dl>\r\n
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annual percentage rate (APR)<\/strong><\/dt>\r\n \t
the yearly interest rate earned by an investment account, also called nominal rate<\/em><\/dd>\r\n<\/dl>\r\n
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annuity<\/strong><\/dt>\r\n \t
an investment in which the purchaser makes a sequence of periodic, equal payments<\/dd>\r\n<\/dl>\r\n
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area<\/strong><\/dt>\r\n \t
in square units, the area formula used in this section is used to find the area of any two-dimensional rectangular region: [latex]A=LW[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
arithmetic sequence<\/strong><\/dt>\r\n \t
a sequence in which the difference between any two consecutive terms is a constant<\/dd>\r\n<\/dl>\r\n
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arithmetic series<\/strong><\/dt>\r\n \t
the sum of the terms in an arithmetic sequence<\/dd>\r\n<\/dl>\r\n
\r\n \t
arrow notation<\/strong><\/dt>\r\n \t
a way to symbolically represent the local and end behavior of a function by using arrows to indicate that an input or output approaches a value<\/dd>\r\n<\/dl>\r\n
\r\n \t
associative property of addition<\/strong><\/dt>\r\n \t
the sum of three numbers may be grouped differently without affecting the result; in symbols, [latex]a+\\left(b+c\\right)=\\left(a+b\\right)+c[\/latex]<\/dd>\r\n<\/dl>\r\n
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associative property of multiplication<\/strong><\/dt>\r\n \t
the product of three numbers may be grouped differently without affecting the result; in symbols, [latex]a\\cdot \\left(b\\cdot c\\right)=\\left(a\\cdot b\\right)\\cdot c[\/latex]<\/dd>\r\n<\/dl>\r\n
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augmented matrix<\/strong><\/dt>\r\n \t
a coefficient matrix adjoined with the constant column separated by a vertical line within the matrix brackets<\/dd>\r\n<\/dl>\r\n
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average rate of change<\/strong><\/dt>\r\n \t
the difference in the output values of a function found for two values of the input divided by the difference between the inputs<\/dd>\r\n<\/dl>\r\n
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axis of symmetry<\/strong><\/dt>\r\n \t
a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by [latex]x=-\\frac{b}{2a}[\/latex].<\/dd>\r\n<\/dl>\r\n
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base<\/strong><\/dt>\r\n \t
in exponential notation, [latex]a^n[\/latex] the expression that is being multiplied<\/dd>\r\n<\/dl>\r\n
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binomial<\/strong><\/dt>\r\n \t
a polynomial containing two terms<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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binomial coefficient<\/strong><\/dt>\r\n \t
the number of ways to choose [latex]r[\/latex] objects from [latex]n[\/latex]\u00a0objects where order does not matter; equivalent to [latex]C\\left(n,r\\right)[\/latex], denoted [latex]\\left(\\begin{gathered}n\\\\ r\\end{gathered}\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
binomial expansion<\/strong><\/dt>\r\n \t
the result of expanding [latex]{\\left(x+y\\right)}^{n}[\/latex] by multiplying<\/dd>\r\n<\/dl>\r\n
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binomial theorem<\/strong><\/dt>\r\n \t
a formula that can be used to expand any binomial<\/dd>\r\n<\/dl>\r\n
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break-even point<\/strong><\/dt>\r\n \t
The point at which a cost function intersects a revenue function; where profit is zero<\/dd>\r\n<\/dl>\r\n
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carrying capacity<\/strong><\/dt>\r\n \t
in a logistic model, the limiting value of the output<\/dd>\r\n<\/dl>\r\n
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Cartesian coordinate system<\/strong><\/dt>\r\n \t
a grid system designed with perpendicular axes invented by Ren\u00e9 Descartes<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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center of an Ellipse<\/strong><\/dt>\r\n \t
The midpoint of both the major and minor axes<\/dd>\r\n<\/dl>\r\n
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center of a Hyperbola<\/strong><\/dt>\r\n \t
The midpoint of both the transverse and conjugate axes of a hyperbola<\/dd>\r\n<\/dl>\r\n
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change-of-base formula<\/strong><\/dt>\r\n \t
a formula for converting a logarithm with any base to a quotient of logarithms with any other base<\/dd>\r\n<\/dl>\r\n
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coefficient<\/strong><\/dt>\r\n \t
any real number [latex]{a}_{i}[\/latex] in a polynomial of the form [latex]{a}_{n}{x}^{n}+\\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[\/latex]<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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coefficient matrix<\/strong><\/dt>\r\n \t
a matrix that contains only the coefficients from a system of equations<\/dd>\r\n<\/dl>\r\n
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column<\/strong><\/dt>\r\n \t
a set of numbers aligned vertically in a matrix<\/dd>\r\n<\/dl>\r\n
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combination<\/strong><\/dt>\r\n \t
a selection of objects in which order does not matter<\/dd>\r\n<\/dl>\r\n
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common difference<\/strong><\/dt>\r\n \t
the difference between any two consecutive terms in an arithmetic sequence<\/dd>\r\n<\/dl>\r\n
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common logarithm<\/strong><\/dt>\r\n \t
the exponent to which [latex]10[\/latex] must be raised to get [latex]x[\/latex]; [latex]{\\mathrm{log}}_{10}\\left(x\\right)[\/latex] is written simply as [latex]\\mathrm{log}\\left(x\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
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common ratio<\/strong><\/dt>\r\n \t
the ratio between any two consecutive terms in a geometric sequence<\/dd>\r\n<\/dl>\r\n
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commutative property of addition<\/strong><\/dt>\r\n \t
two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[\/latex]<\/dd>\r\n<\/dl>\r\n
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commutative property of multiplication<\/strong><\/dt>\r\n \t
two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\\cdot b=b\\cdot a[\/latex]<\/dd>\r\n<\/dl>\r\n
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complement of an event<\/strong><\/dt>\r\n \t
the set of outcomes in the sample space that are not in the event [latex]E[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
completing the square<\/strong><\/dt>\r\n \t
a process for solving quadratic equations in which terms are added to or subtracted from both sides of the equation in order to make one side a perfect square<\/dd>\r\n<\/dl>\r\n
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complex conjugate<\/strong><\/dt>\r\n \t
the complex number in which the sign of the imaginary part is changed and the real part of the number is left unchanged; when added to or multiplied by the original complex number, the result is a real number<\/dd>\r\n<\/dl>\r\n
\r\n \t
complex number<\/strong><\/dt>\r\n \t
the sum of a real number and an imaginary number, written in the standard form [latex]a+bi[\/latex], where [latex]a[\/latex] is the real part, and [latex]bi[\/latex] is the imaginary part<\/dd>\r\n<\/dl>\r\n
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complex plane<\/strong><\/dt>\r\n \t
a coordinate system in which the horizontal axis is used to represent the real part of a complex number and the vertical axis is used to represent the imaginary part of a complex number<\/dd>\r\n<\/dl>\r\n
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complex roots<\/strong><\/dt>\r\n \t
Solutions to a quadratic equation that contain imaginary numbers, occurring when the discriminant is negative<\/dd>\r\n<\/dl>\r\n
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composite function<\/strong><\/dt>\r\n \t
the new function formed by function composition, when the output of one function is used as the input of another<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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compound inequality<\/strong><\/dt>\r\n \t
a problem or a statement that includes two inequalities<\/dd>\r\n<\/dl>\r\n
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compound interest<\/strong><\/dt>\r\n \t
interest earned on the total balance, not just the principal<\/dd>\r\n<\/dl>\r\n
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conic Section<\/strong><\/dt>\r\n \t
Any shape resulting from the intersection of a right circular cone with a plane<\/dd>\r\n<\/dl>\r\n
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conjugate Axis<\/strong><\/dt>\r\n \t
The axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints<\/dd>\r\n<\/dl>\r\n
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conjugate pair<\/strong><\/dt>\r\n \t
Two complex numbers in the form [latex]a + bi[\/latex] and [latex]a - bi[\/latex] that occur as solutions to quadratic equations with complex roots<\/dd>\r\n<\/dl>\r\n
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consistent system<\/strong><\/dt>\r\n \t
A system for which there is a single solution to all equations in the system and it is an independent system, or if there are an infinite number of solutions and it is a dependent system<\/dd>\r\n<\/dl>\r\n
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constant<\/strong><\/dt>\r\n \t
a quantity that does not change value<\/dd>\r\n<\/dl>\r\n
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constant of variation<\/strong><\/dt>\r\n \t
the non-zero value [latex]k[\/latex]\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\r\n<\/dl>\r\n
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continuous function<\/strong><\/dt>\r\n \t
a function whose graph can be drawn without lifting the pen from the paper because there are no breaks in the graph<\/dd>\r\n<\/dl>\r\n
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cost function<\/strong><\/dt>\r\n \t
The function used to calculate the costs of doing business; it usually has two parts, fixed costs and variable costs<\/dd>\r\n<\/dl>\r\n
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correlation coefficient<\/strong><\/dt>\r\n \t
a value, [latex]r[\/latex], between [latex]\u20131[\/latex] and [latex]1[\/latex] that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.<\/dd>\r\n<\/dl>\r\n
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cross-multiplication<\/strong><\/dt>\r\n \t
A method for solving rational equations set up as a proportion by multiplying terms across the equal sign.<\/dd>\r\n<\/dl>\r\n
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decreasing function<\/strong><\/dt>\r\n \t
a function is decreasing in some open interval if [latex]f\\left(b\\right)<f\\left(a\\right)[\/latex] for any two input values [latex]a[\/latex] and [latex]b[\/latex] in the given interval where [latex]b>a[\/latex]<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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decreasing linear function<\/strong><\/dt>\r\n \t
a function with a negative slope: If [latex]m<0, \\text{then }f\\left(x\\right)=mx+b[\/latex] is decreasing.<\/dd>\r\n<\/dl>\r\n
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degree<\/strong><\/dt>\r\n \t
the highest power of the variable that occurs in a polynomial<\/dd>\r\n<\/dl>\r\n
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dependent system<\/strong><\/dt>\r\n \t
A system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system<\/dd>\r\n<\/dl>\r\n
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dependent variable<\/strong><\/dt>\r\n \t
an output variable<\/dd>\r\n<\/dl>\r\n
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Descartes\u2019 Rule of Signs<\/strong><\/dt>\r\n \t
a rule that determines the maximum possible numbers of positive and negative real zeros based on the number of sign changes of [latex]f\\left(x\\right)[\/latex] and [latex]f\\left(-x\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
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difference of squares<\/strong><\/dt>\r\n \t
the binomial that results when a binomial is multiplied by a binomial with the same terms, but the opposite sign<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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direct variation<\/strong><\/dt>\r\n \t
the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\r\n<\/dl>\r\n
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directrix<\/strong><\/dt>\r\n \t
a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant<\/dd>\r\n<\/dl>\r\n
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discriminant<\/strong><\/dt>\r\n \t
the value under the radical in the quadratic formula, [latex]b^2-4ac[\/latex], which tells whether the quadratic has real or complex roots<\/dd>\r\n<\/dl>\r\n
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distance formula<\/strong><\/dt>\r\n \t
a formula that can be used to find the length of a line segment if the endpoints are known<\/dd>\r\n<\/dl>\r\n
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<\/dt>\r\n<\/dl>\r\n
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distributive property<\/strong><\/dt>\r\n \t
the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, [latex]a\\cdot \\left(b+c\\right)=a\\cdot b+a\\cdot c[\/latex]<\/dd>\r\n<\/dl>\r\n
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Division Algorithm<\/strong><\/dt>\r\n \t
given a polynomial dividend [latex]f\\left(x\\right)[\/latex]\u00a0and a non-zero polynomial divisor [latex]d\\left(x\\right)[\/latex]\u00a0where the degree of [latex]d\\left(x\\right)[\/latex]\u00a0is less than or equal to the degree of [latex]f\\left(x\\right)[\/latex],\u00a0there exist unique polynomials [latex]q\\left(x\\right)[\/latex]\u00a0and [latex]r\\left(x\\right)[\/latex]\u00a0such that [latex]f\\left(x\\right)=d\\left(x\\right)q\\left(x\\right)+r\\left(x\\right)[\/latex]\u00a0where [latex]q\\left(x\\right)[\/latex]\u00a0is the quotient and [latex]r\\left(x\\right)[\/latex]\u00a0is the remainder. The remainder is either equal to zero or has degree strictly less than [latex]d\\left(x\\right)[\/latex].<\/dd>\r\n<\/dl>\r\n
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diverge<\/strong><\/dt>\r\n \t
a series is said to diverge if the sum is not a real number<\/dd>\r\n<\/dl>\r\n
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domain<\/strong><\/dt>\r\n \t
the set of all possible input values for a relation<\/dd>\r\n<\/dl>\r\n
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doubling time<\/strong><\/dt>\r\n \t
the time it takes for a quantity to double<\/dd>\r\n<\/dl>\r\n
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ellipse<\/strong><\/dt>\r\n \t
The set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the sum of their distances from two fixed points is a constant<\/dd>\r\n<\/dl>\r\n
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end behavior<\/strong><\/dt>\r\n \t
the behavior of the graph of a function as the input decreases without bound and increases without bound<\/dd>\r\n<\/dl>\r\n
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entry<\/strong><\/dt>\r\n \t
an element, coefficient, or constant in a matrix<\/dd>\r\n<\/dl>\r\n
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<\/dt>\r\n \t
equation<\/strong><\/dt>\r\n \t
a mathematical statement indicating that two expressions are equal<\/dd>\r\n<\/dl>\r\n
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equation in two variables<\/strong><\/dt>\r\n \t
a mathematical statement, typically written in x <\/em>and y<\/em>, in which two expressions are equal<\/dd>\r\n<\/dl>\r\n
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even function<\/strong><\/dt>\r\n \t
a function whose graph is unchanged by horizontal reflection, [latex]f\\left(x\\right)=f\\left(-x\\right)[\/latex], and is symmetric about the [latex]y\\text{-}[\/latex] axis<\/dd>\r\n<\/dl>\r\n
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event<\/strong><\/dt>\r\n \t
any subset of a sample space<\/dd>\r\n<\/dl>\r\n
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excluded values<\/strong><\/dt>\r\n \t
Values that make the denominator in a rational expression equal to zero, which must be excluded from the solution set.<\/dd>\r\n<\/dl>\r\n
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experiment<\/strong><\/dt>\r\n \t
an activity with an observable result<\/dd>\r\n<\/dl>\r\n
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explicit formula<\/strong><\/dt>\r\n \t
a formula that defines each term of a sequence in terms of its position in the sequence<\/dd>\r\n<\/dl>\r\n
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exponent<\/strong><\/dt>\r\n \t
in exponential notation, the raised number or variable that indicates how many times the base is being multiplied<\/dd>\r\n<\/dl>\r\n
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exponential growth<\/strong><\/dt>\r\n \t
a model that grows by a rate proportional to the amount present<\/dd>\r\n<\/dl>\r\n
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exponential notation<\/strong><\/dt>\r\n \t
a shorthand method of writing products of the same factor<\/dd>\r\n<\/dl>\r\n
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extraneous solution<\/strong><\/dt>\r\n \t
a solution introduced while solving an equation that does not satisfy the conditions of the original equation<\/dd>\r\n<\/dl>\r\n
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extrapolation<\/strong><\/dt>\r\n \t
predicting a value outside the domain and range of the data<\/dd>\r\n<\/dl>\r\n
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factor by grouping<\/strong><\/dt>\r\n \t
a method for factoring a trinomial of the form [latex]a{x}^{2}+bx+c[\/latex] by dividing the x<\/em> term into the sum of two terms, factoring each portion of the expression separately, and then factoring out the GCF of the entire expression<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
Factor Theorem<\/strong><\/dt>\r\n \t
k<\/em>\u00a0is a zero of polynomial function [latex]f\\left(x\\right)[\/latex] if and only if [latex]\\left(x-k\\right)[\/latex] \u00a0is a factor of [latex]f\\left(x\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
finite sequence<\/strong><\/dt>\r\n \t
a function whose domain consists of a finite subset of the positive integers [latex]\\left\\{1,2,\\dots n\\right\\}[\/latex] for some positive integer [latex]n[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
focal diameter (latus rectum)<\/strong><\/dt>\r\n \t
the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola<\/dd>\r\n<\/dl>\r\n
\r\n \t
foci<\/strong><\/dt>\r\n \t
Plural of focus<\/dd>\r\n<\/dl>\r\n
\r\n \t
focus (of an ellipse)<\/strong><\/dt>\r\n \t
One of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point [latex]\\left(x,y\\right)[\/latex] on the ellipse is a constant<\/dd>\r\n<\/dl>\r\n
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focus (of a parabola)<\/strong><\/dt>\r\n \t
a fixed point in the interior of a parabola that lies on the axis of symmetry<\/dd>\r\n<\/dl>\r\n
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formula<\/strong><\/dt>\r\n \t
an equation expressing a relationship between constant and variable quantities<\/dd>\r\n<\/dl>\r\n
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function<\/strong><\/dt>\r\n \t
a relation in which each input value yields a unique output value<\/dd>\r\n<\/dl>\r\n
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fundamental counting principle<\/strong><\/dt>\r\n \t
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Multiplication Principle<\/dd>\r\n<\/dl>\r\n
\r\n \t
Fundamental Theorem of Algebra<\/strong><\/dt>\r\n \t
a polynomial function with degree greater than 0 has at least one complex zero<\/dd>\r\n<\/dl>\r\n
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Gaussian elimination<\/strong><\/dt>\r\n \t
using elementary row operations to obtain a matrix in row-echelon form<\/dd>\r\n<\/dl>\r\n
\r\n \t
general form of a quadratic function<\/strong><\/dt>\r\n \t
the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex], where [latex]a[\/latex], [latex]b[\/latex], and [latex]c[\/latex]\u00a0are real numbers and [latex]a\\ne 0[\/latex].<\/dd>\r\n<\/dl>\r\n
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geometric sequence<\/strong><\/dt>\r\n \t
a sequence in which the ratio of a term to a previous term is a constant<\/dd>\r\n<\/dl>\r\n
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geometric series<\/strong><\/dt>\r\n \t
the sum of the terms in a geometric sequence<\/dd>\r\n<\/dl>\r\n
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global maximum<\/strong><\/dt>\r\n \t
highest turning point on a graph; [latex]f\\left(a\\right)[\/latex]\u00a0where [latex]f\\left(a\\right)\\ge f\\left(x\\right)[\/latex]\u00a0for all [latex]x[\/latex].<\/dd>\r\n<\/dl>\r\n
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global minimum<\/b><\/dt>\r\n \t
lowest turning point on a graph; [latex]f\\left(a\\right)[\/latex]\u00a0where [latex]f\\left(a\\right)\\le f\\left(x\\right)[\/latex] for all [latex]x[\/latex].<\/dd>\r\n<\/dl>\r\n
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graph in two variables<\/strong><\/dt>\r\n \t
the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane<\/dd>\r\n<\/dl>\r\n
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greatest common factor<\/strong><\/dt>\r\n \t
the largest polynomial that divides evenly into each polynomial<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
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half-life<\/strong><\/dt>\r\n \t
the length of time it takes for a substance to exponentially decay to half of its original quantity<\/dd>\r\n<\/dl>\r\n
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horizontal asymptote<\/strong><\/dt>\r\n \t
a horizontal line [latex]y=b[\/latex]\u00a0where the graph approaches the line as the inputs increase or decrease without bound.<\/dd>\r\n<\/dl>\r\n
\r\n \t
horizontal compression<\/strong><\/dt>\r\n \t
a transformation that compresses a function\u2019s graph horizontally, by multiplying the input by a constant [latex]b>1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
horizontal line<\/strong><\/dt>\r\n \t
a line defined by [latex]f\\left(x\\right)=b[\/latex] where [latex]b[\/latex] is a real number. The slope of a horizontal line is [latex]0[\/latex].<\/dd>\r\n<\/dl>\r\n
\r\n \t
horizontal line test<\/strong><\/dt>\r\n \t
a method of testing whether a function is one-to-one by determining whether any horizontal line intersects the graph more than once<\/dd>\r\n<\/dl>\r\n
\r\n \t
horizontal reflection<\/strong><\/dt>\r\n \t
a transformation that reflects a function\u2019s graph across the y<\/em>-axis by multiplying the input by [latex]-1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
horizontal shift<\/strong><\/dt>\r\n \t
a transformation that shifts a function\u2019s graph left or right by adding a positive or negative constant to the input<\/dd>\r\n<\/dl>\r\n
\r\n \t
horizontal stretch<\/strong><\/dt>\r\n \t
a transformation that stretches a function\u2019s graph horizontally by multiplying the input by a constant [latex]0<b<1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
hyperbola<\/strong><\/dt>\r\n \t
The set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the difference of the distances between [latex]\\left(x,y\\right)[\/latex] and the foci is a positive constant<\/dd>\r\n<\/dl>\r\n
\r\n \t
identity matrix<\/strong><\/dt>\r\n \t
a square matrix containing ones down the main diagonal and zeros everywhere else; it acts as a 1 in matrix algebra<\/dd>\r\n<\/dl>\r\n
\r\n \t
identity property of addition<\/strong><\/dt>\r\n \t
there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, [latex]a+0=a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
identity property of multiplication<\/strong><\/dt>\r\n \t
there is a unique number, called the multiplicative identity, [latex]1[\/latex], which, when multiplied by a number, results in the original number; in symbols, [latex]a\\cdot 1=a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
imaginary number<\/strong><\/dt>\r\n \t
a number in the form [latex]bi[\/latex]\u00a0where [latex]i=\\sqrt{-1}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
inconsistent system<\/strong><\/dt>\r\n \t
A system of linear equations with no common solution because they represent parallel lines, which have no point or line in common<\/dd>\r\n<\/dl>\r\n
\r\n \t
increasing function<\/strong><\/dt>\r\n \t
a function is increasing in some open interval if [latex]f\\left(b\\right)>f\\left(a\\right)[\/latex] for any two input values [latex]a[\/latex] and [latex]b[\/latex] in the given interval where [latex]b>a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
increasing linear function<\/strong><\/dt>\r\n \t
a function with a positive slope: If [latex]m>0, \\text{then }f\\left(x\\right)=mx+b[\/latex] is increasing.<\/dd>\r\n<\/dl>\r\n
\r\n \t
independent system<\/strong><\/dt>\r\n \t
A system of linear equations with exactly one solution pair [latex]\\left(x,y\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
independent variable<\/strong><\/dt>\r\n \t
an input variable<\/dd>\r\n<\/dl>\r\n
\r\n \t
index<\/strong><\/dt>\r\n \t
the number above the radical sign indicating the n<\/em>th root<\/dd>\r\n<\/dl>\r\n
\r\n \t
index of summation<\/strong><\/dt>\r\n \t
in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation<\/dd>\r\n<\/dl>\r\n
\r\n \t
infinite sequence<\/strong><\/dt>\r\n \t
a function whose domain is the set of positive integers<\/dd>\r\n<\/dl>\r\n
\r\n \t
infinite series<\/strong><\/dt>\r\n \t
the sum of the terms in an infinite sequence<\/dd>\r\n<\/dl>\r\n
\r\n \t
input<\/strong><\/dt>\r\n \t
each object or value in a domain that relates to another object or value by a relationship known as a function<\/dd>\r\n<\/dl>\r\n
\r\n \t
integers<\/strong><\/dt>\r\n \t
the set consisting of the natural numbers, their opposites, and [latex]0[\/latex]: [latex]\\{\\dots ,-3,-2,-1,0,1,2,3,\\dots \\}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
<\/dd>\r\n<\/dl>\r\n
\r\n \t
intercepts<\/strong><\/dt>\r\n \t
the points at which the graph of an equation crosses the x<\/em>-axis and the y<\/em>-axis<\/dd>\r\n<\/dl>\r\n
\r\n \t
Intermediate Value Theorem<\/strong><\/dt>\r\n \t
for two numbers [latex]a[\/latex]\u00a0and [latex]b[\/latex]\u00a0in the domain of [latex]f[\/latex],\u00a0if [latex]a<b[\/latex]\u00a0and [latex]f\\left(a\\right)\\ne f\\left(b\\right)[\/latex],\u00a0then the function [latex]f[\/latex]\u00a0takes on every value between [latex]f\\left(a\\right)[\/latex]\u00a0and [latex]f\\left(b\\right)[\/latex];\u00a0specifically, when a polynomial function changes from a negative value to a positive value, the function must cross the [latex]x[\/latex]-axis<\/dd>\r\n<\/dl>\r\n
\r\n \t
interpolation<\/strong><\/dt>\r\n \t
predicting a value inside the domain and range of the data<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
interval<\/strong><\/dt>\r\n \t
an interval describes a set of numbers where a solution falls<\/dd>\r\n<\/dl>\r\n
\r\n \t
interval notation<\/strong><\/dt>\r\n \t
a mathematical statement that describes a solution set and uses parentheses or brackets to indicate where an interval begins and ends<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
inverse function<\/strong><\/dt>\r\n \t
for any one-to-one function [latex]f\\left(x\\right)[\/latex], the inverse is a function [latex]{f}^{-1}\\left(x\\right)[\/latex] such that [latex]{f}^{-1}\\left(f\\left(x\\right)\\right)=x[\/latex] for all [latex]x[\/latex] in the domain of [latex]f[\/latex]; this also implies that [latex]f\\left({f}^{-1}\\left(x\\right)\\right)=x[\/latex] for all [latex]x[\/latex] in the domain of [latex]{f}^{-1}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
inverse property of addition<\/strong><\/dt>\r\n \t
for every real number [latex]a[\/latex], there is a unique number, called the additive inverse (or opposite), denoted [latex]-a[\/latex], which, when added to the original number, results in the additive identity, 0; in symbols, [latex]a+\\left(-a\\right)=0[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
inverse property of multiplication<\/strong><\/dt>\r\n \t
for every non-zero real number [latex]a[\/latex], there is a unique number, called the multiplicative inverse (or reciprocal), denoted [latex]\\dfrac{1}{a}[\/latex], which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, [latex]a\\cdot \\dfrac{1}{a}=1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
inverse variation<\/strong><\/dt>\r\n \t
the relationship between two variables in which the product of the variables is a constant<\/dd>\r\n<\/dl>\r\n
\r\n \t
inversely proportional<\/strong><\/dt>\r\n \t
a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\r\n<\/dl>\r\n
\r\n \t
invertible function<\/strong><\/dt>\r\n \t
any function that has an inverse function<\/dd>\r\n<\/dl>\r\n
\r\n \t
irrational numbers<\/strong><\/dt>\r\n \t
the set of all numbers that are not rational; they cannot be written as either a terminating or repeating decimal; they cannot be expressed as a fraction of two integers<\/dd>\r\n<\/dl>\r\n
\r\n \t
joint variation<\/strong><\/dt>\r\n \t
a relationship where a variable varies directly or inversely with multiple variables<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
leading coefficient<\/strong><\/dt>\r\n \t
the coefficient of the leading term<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
leading term<\/strong><\/dt>\r\n \t
\u00a0the term containing the highest degree<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
least common denominator<\/strong><\/dt>\r\n \t
the smallest multiple that two denominators have in common<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
least squares regression<\/strong><\/dt>\r\n \t
a statistical technique for fitting a line to data in a way that minimizes the differences between the line and data values<\/dd>\r\n<\/dl>\r\n
\r\n \t
Linear Factorization Theorem<\/strong><\/dt>\r\n<\/dl>\r\n
\r\n \t
allowing for multiplicities, a polynomial function will have the same number of factors as its degree, and each factor will be in the form [latex]\\left(x-c\\right)[\/latex] where c<\/em>\u00a0is a complex number<\/dd>\r\n<\/dl>\r\n
\r\n \t
linear function<\/strong><\/dt>\r\n \t
a function with a constant rate of change that is a polynomial of degree [latex]1[\/latex] whose graph is a straight line<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
linear inequality<\/strong><\/dt>\r\n \t
similar to a linear equation except that the solutions will include an interval of numbers<\/dd>\r\n<\/dl>\r\n
\r\n \t
local extrema<\/strong><\/dt>\r\n \t
collectively, all of a function's local maxima and minima<\/dd>\r\n<\/dl>\r\n
\r\n \t
local maximum<\/strong><\/dt>\r\n \t
a value of the input where a function changes from increasing to decreasing as the input value increases.<\/dd>\r\n<\/dl>\r\n
\r\n \t
local minimum<\/strong><\/dt>\r\n \t
a value of the input where a function changes from decreasing to increasing as the input value increases.<\/dd>\r\n<\/dl>\r\n
\r\n \t
logarithm<\/strong><\/dt>\r\n \t
the exponent to which [latex]b[\/latex]\u00a0must be raised to get [latex]x[\/latex]; written [latex]y={\\mathrm{log}}_{b}\\left(x\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
logistic growth model<\/strong><\/dt>\r\n \t
a function of the form [latex]f\\left(x\\right)=\\frac{c}{1+a{e}^{-bx}}[\/latex] where [latex]\\frac{c}{1+a}[\/latex] is the initial value, c<\/em>\u00a0is the carrying capacity, or limiting value, and b<\/em>\u00a0is a constant determined by the rate of growth<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
lower limit of summation<\/strong><\/dt>\r\n \t
the number used in the explicit formula to find the first term in a series<\/dd>\r\n<\/dl>\r\n
\r\n \t
main diagonal<\/strong><\/dt>\r\n \t
entries from the upper left corner diagonally to the lower right corner of a square matrix<\/dd>\r\n<\/dl>\r\n
\r\n \t
major Axis<\/strong><\/dt>\r\n \t
The longer of the two axes of an ellipse<\/dd>\r\n<\/dl>\r\n
\r\n \t
matrix<\/strong><\/dt>\r\n \t
a rectangular array of numbers<\/dd>\r\n<\/dl>\r\n
\r\n \t
midpoint formula<\/strong><\/dt>\r\n \t
\u00a0a formula to find the point that divides a line segment into two parts of equal length<\/dd>\r\n<\/dl>\r\n
\r\n \t
minor Axis<\/strong><\/dt>\r\n \t
The shorter of the two axes of an ellipse<\/dd>\r\n<\/dl>\r\n
\r\n \t
model breakdown<\/strong><\/dt>\r\n \t
when a model no longer applies after a certain point<\/dd>\r\n<\/dl>\r\n
\r\n \t
monomial<\/strong><\/dt>\r\n \t
a polynomial containing one term<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
multiplication principle<\/strong><\/dt>\r\n \t
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Fundamental Counting Principle<\/dd>\r\n<\/dl>\r\n
\r\n \t
multiplicative inverse of a matrix<\/strong><\/dt>\r\n \t
a matrix that, when multiplied by the original, equals the identity matrix<\/dd>\r\n<\/dl>\r\n
\r\n \t
multiplicity<\/strong><\/dt>\r\n \t
the number of times a given factor appears in the factored form of the equation of a polynomial; if a polynomial contains a factor of the form [latex]{\\left(x-h\\right)}^{p}[\/latex], [latex]x=h[\/latex]\u00a0is a zero of multiplicity [latex]p[\/latex].<\/dd>\r\n<\/dl>\r\n
\r\n \t
mutually exclusive events<\/strong><\/dt>\r\n \t
events that have no outcomes in common<\/dd>\r\n<\/dl>\r\n
\r\n \t
natural logarithm<\/strong><\/dt>\r\n \t
the exponent to which the number [latex]e[\/latex]\u00a0must be raised to get [latex]x[\/latex]; [latex]{\\mathrm{log}}_{e}\\left(x\\right)[\/latex] is written as [latex]\\mathrm{ln}\\left(x\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
natural numbers<\/strong><\/dt>\r\n \t
the set of counting numbers: [latex]\\{1,2,3,\\dots \\}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
Newton\u2019s Law of Cooling<\/strong><\/dt>\r\n \t
the scientific formula for temperature as a function of time as an object\u2019s temperature is equalized with the ambient temperature<\/dd>\r\n<\/dl>\r\n
\r\n \t
[latex]n[\/latex] factorial<\/strong><\/dt>\r\n \t
the product of all the positive integers from 1 to [latex]n[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
nominal rate<\/strong><\/dt>\r\n \t
the yearly interest rate earned by an investment account, also called annual percentage rate<\/em><\/dd>\r\n<\/dl>\r\n
\r\n \t
[latex]n[\/latex]th partial sum<\/strong><\/dt>\r\n \t
the sum of the first [latex]n[\/latex] terms of a sequence<\/dd>\r\n<\/dl>\r\n
\r\n \t
[latex]n[\/latex]th term of a sequence<\/strong><\/dt>\r\n \t
a formula for the general term of a sequence<\/dd>\r\n<\/dl>\r\n
\r\n \t
odd function<\/strong><\/dt>\r\n \t
a function whose graph is unchanged by combined horizontal and vertical reflection, [latex]f\\left(x\\right)=-f\\left(-x\\right)[\/latex], and is symmetric about the origin<\/dd>\r\n<\/dl>\r\n
\r\n \t
one-to-one function<\/strong><\/dt>\r\n \t
a function for which each value of the output is associated with a unique input value<\/dd>\r\n<\/dl>\r\n
\r\n \t
order of magnitude<\/strong><\/dt>\r\n \t
the power of ten when a number is expressed in scientific notation with one non-zero digit to the left of the decimal<\/dd>\r\n<\/dl>\r\n
\r\n \t
order of operations<\/strong><\/dt>\r\n \t
a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
ordered pair<\/strong><\/dt>\r\n \t
a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, [latex]\\left(x,y\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
origin<\/strong><\/dt>\r\n \t
the point where the two axes cross in the center of the plane, described by the ordered pair [latex]\\left(0,0\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
outcomes<\/strong><\/dt>\r\n \t
the possible results of an experiment<\/dd>\r\n<\/dl>\r\n
\r\n \t
output<\/strong><\/dt>\r\n \t
each object or value in the range that is produced when an input value is entered into a function<\/dd>\r\n<\/dl>\r\n
\r\n \t
parabola<\/strong><\/dt>\r\n \t
the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix<\/dd>\r\n<\/dl>\r\n
\r\n \t
parallel lines<\/strong><\/dt>\r\n \t
two or more lines with the same slope<\/dd>\r\n<\/dl>\r\n
\r\n \t
partial fractions<\/strong><\/dt>\r\n \t
\u00a0the individual fractions that make up the sum or difference of a rational expression before combining them into a simplified rational expression<\/dd>\r\n<\/dl>\r\n
\r\n \t
partial fraction decomposition<\/strong><\/dt>\r\n \t
the process of returning a simplified rational expression to its original form, a sum or difference of simpler rational expressions<\/dd>\r\n<\/dl>\r\n
\r\n \t
perfect square trinomial<\/strong><\/dt>\r\n \t
the trinomial that results when a binomial is squared<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
perimeter<\/strong><\/dt>\r\n \t
in linear units, the perimeter formula is used to find the linear measurement, or outside length and width, around a two-dimensional regular object; for a rectangle: [latex]P=2L+2W[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
permutation<\/strong><\/dt>\r\n \t
a selection of objects in which order matters<\/dd>\r\n<\/dl>\r\n
\r\n \t
perpendicular lines<\/strong><\/dt>\r\n \t
two lines that intersect at right angles and have slopes that are negative reciprocals of each other<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
piecewise function<\/strong><\/dt>\r\n \t
a function in which more than one formula is used to define the output<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
point-slope form<\/strong><\/dt>\r\n \t
the equation of a linear function of the form [latex]y-{y}_{1}=m\\left(x-{x}_{1}\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
polynomial<\/strong><\/dt>\r\n \t
a sum of terms each consisting of a variable raised to a nonnegative integer power<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
polynomial function<\/strong><\/dt>\r\n \t
a function that consists of either zero or the sum of a finite number of non-zero\u00a0terms, each of which is a product of a number, called the\u00a0coefficient\u00a0of the term, and a variable raised to a non-negative integer power.<\/dd>\r\n<\/dl>\r\n
\r\n \t
polynomial equation<\/strong><\/dt>\r\n \t
an equation containing a string of terms including numerical coefficients and variables raised to whole-number exponents<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
power function<\/strong><\/dt>\r\n \t
a function that can be represented in the form [latex]f\\left(x\\right)=a{x}^{n}[\/latex]\u00a0where a\u00a0<\/em>is a constant, the base is a variable, and the exponent is\u00a0n<\/i>,\u00a0is a smooth curve represented by a graph with no sharp corners<\/dd>\r\n<\/dl>\r\n
\r\n \t
power rule for logarithms<\/strong><\/dt>\r\n \t
a rule of logarithms that states that the log of a power is equal to the product of the exponent and the log of its base<\/dd>\r\n<\/dl>\r\n
\r\n \t
principal n<\/em>th root<\/strong><\/dt>\r\n \t
the number with the same sign as [latex]a[\/latex] that when raised to the n<\/em>th power equals [latex]a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
principal square root<\/strong><\/dt>\r\n \t
the nonnegative square root of a number [latex]a[\/latex] that, when multiplied by itself, equals [latex]a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
probability<\/strong><\/dt>\r\n \t
a number from [latex]0[\/latex] to [latex]1[\/latex] indicating the likelihood of an event<\/dd>\r\n<\/dl>\r\n
\r\n \t
probability model<\/strong><\/dt>\r\n \t
a mathematical description of an experiment listing all possible outcomes and their associated probabilities<\/dd>\r\n<\/dl>\r\n
\r\n \t
product rule for logarithms<\/strong><\/dt>\r\n \t
a rule of logarithms that states that the log of a product is equal to a sum of logarithms<\/dd>\r\n<\/dl>\r\n
\r\n \t
profit function<\/strong><\/dt>\r\n \t
The profit function is written as [latex]P\\left(x\\right)=R\\left(x\\right)-C\\left(x\\right)[\/latex], revenue minus cost<\/dd>\r\n<\/dl>\r\n
\r\n \t
projectile motion<\/strong><\/dt>\r\n \t
motion of an object thrown or launched near Earth's surface<\/dd>\r\n<\/dl>\r\n
\r\n \t
Pythagorean Theorem<\/strong><\/dt>\r\n \t
a theorem that states the relationship among the lengths of the sides of a right triangle, used to solve right triangle problems<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
quadrant<\/strong><\/dt>\r\n \t
one quarter of the coordinate plane, created when the axes divide the plane into four sections<\/dd>\r\n<\/dl>\r\n
\r\n \t
quadratic equation<\/strong><\/dt>\r\n \t
an equation containing a second-degree polynomial; can be solved using multiple methods<\/dd>\r\n<\/dl>\r\n
\r\n \t
quadratic formula<\/strong><\/dt>\r\n \t
a formula that will solve all quadratic equations<\/dd>\r\n<\/dl>\r\n
\r\n \t
quadratic function<\/strong><\/dt>\r\n \t
A polynomial function of degree 2<\/dd>\r\n<\/dl>\r\n
\r\n \t
quotient rule for logarithms<\/strong><\/dt>\r\n \t
a rule of logarithms that states that the log of a quotient is equal to a difference of logarithms<\/dd>\r\n<\/dl>\r\n
\r\n \t
radical<\/strong><\/dt>\r\n \t
the symbol used to indicate a root<\/dd>\r\n<\/dl>\r\n
\r\n \t
radical equation<\/strong><\/dt>\r\n \t
an equation containing at least one radical term where the variable is part of the radicand<\/dd>\r\n<\/dl>\r\n
\r\n \t
radical expression<\/strong><\/dt>\r\n \t
an expression containing a radical symbol<\/dd>\r\n<\/dl>\r\n
\r\n \t
radicand<\/strong><\/dt>\r\n \t
the number under the radical symbol<\/dd>\r\n<\/dl>\r\n
\r\n \t
range<\/strong><\/dt>\r\n \t
the set of output values that result from the input values in a relation<\/dd>\r\n<\/dl>\r\n
\r\n \t
rate<\/strong><\/dt>\r\n \t
speed or frequency at which something occurs<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
rate of change<\/strong><\/dt>\r\n \t
the change of an output quantity relative to the change of the input quantity<\/dd>\r\n<\/dl>\r\n
\r\n \t
rational equation<\/strong><\/dt>\r\n \t
An equation that contains at least one rational expression, where the variable appears in at least one of the denominators.<\/dd>\r\n<\/dl>\r\n
\r\n \t
rational expression<\/strong><\/dt>\r\n \t
The ratio or quotient of two polynomials, e.g., \\( \\frac{x+1}{x^2-4} \\), \\( \\frac{1}{x-3} \\), or \\( \\frac{4}{x^2+x-2} \\).<\/dd>\r\n<\/dl>\r\n
\r\n \t
rational function<\/strong><\/dt>\r\n \t
a function that can be written as the ratio of two polynomials<\/dd>\r\n<\/dl>\r\n
\r\n \t
rational numbers<\/strong><\/dt>\r\n \t
the set of all numbers of the form [latex]\\dfrac{m}{n}[\/latex], where [latex]m[\/latex] and [latex]n[\/latex] are integers and [latex]n\\ne 0[\/latex]. Any rational number may be written as a fraction or a terminating or repeating decimal.<\/dd>\r\n<\/dl>\r\n
\r\n \t
Rational Zero Theorem<\/strong><\/dt>\r\n \t
the possible rational zeros of a polynomial function have the form [latex]\\frac{p}{q}[\/latex] where p<\/em>\u00a0is a factor of the constant term and q<\/em>\u00a0is a factor of the leading coefficient<\/dd>\r\n<\/dl>\r\n
\r\n \t
real number line<\/strong><\/dt>\r\n \t
a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.<\/dd>\r\n<\/dl>\r\n
\r\n \t
real numbers<\/strong><\/dt>\r\n \t
the sets of rational numbers and irrational numbers taken together<\/dd>\r\n<\/dl>\r\n
\r\n \t
recursive formula<\/strong><\/dt>\r\n \t
a formula that defines each term of a sequence using previous term(s)<\/dd>\r\n<\/dl>\r\n
\r\n \t
relation<\/strong><\/dt>\r\n \t
a set of ordered pairs<\/dd>\r\n<\/dl>\r\n
\r\n \t
Remainder Theorem<\/strong><\/dt>\r\n \t
if a polynomial [latex]f\\left(x\\right)[\/latex] is divided by [latex]x-k[\/latex] , then the remainder is equal to the value [latex]f\\left(k\\right)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
removable discontinuity<\/strong><\/dt>\r\n \t
a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function<\/dd>\r\n<\/dl>\r\n
\r\n \t
revenue function<\/strong><\/dt>\r\n \t
The function that is used to calculate revenue, simply written as [latex]R=xp[\/latex], where [latex]x=[\/latex] quantity and [latex]p=[\/latex] price<\/dd>\r\n<\/dl>\r\n
\r\n \t
row<\/strong><\/dt>\r\n \t
a set of numbers aligned horizontally in a matrix<\/dd>\r\n<\/dl>\r\n
\r\n \t
row-echelon form<\/strong><\/dt>\r\n \t
after performing row operations, the matrix form that contains ones down the main diagonal and zeros at every space below the diagonal<\/dd>\r\n<\/dl>\r\n
\r\n \t
row-equivalent<\/strong><\/dt>\r\n \t
two matrices [latex]A[\/latex] and [latex]B[\/latex] are row-equivalent if one can be obtained from the other by performing basic row operations<\/dd>\r\n<\/dl>\r\n
\r\n \t
row operations<\/strong><\/dt>\r\n \t
adding one row to another row, multiplying a row by a constant, interchanging rows, and so on, with the goal of achieving row-echelon form<\/dd>\r\n<\/dl>\r\n
\r\n \t
sample space<\/strong><\/dt>\r\n \t
the set of all possible outcomes of an experiment<\/dd>\r\n<\/dl>\r\n
\r\n \t
scalar multiple<\/strong><\/dt>\r\n \t
an entry of a matrix that has been multiplied by a scalar<\/dd>\r\n<\/dl>\r\n
\r\n \t
scientific notation<\/strong><\/dt>\r\n \t
a shorthand notation for writing very large or very small numbers in the form [latex]a\\times {10}^{n}[\/latex] where [latex]1\\le |a|<10[\/latex] and [latex]n[\/latex] is an integer<\/dd>\r\n<\/dl>\r\n
\r\n \t
sequence<\/strong><\/dt>\r\n \t
a function whose domain is a subset of the positive integers<\/dd>\r\n<\/dl>\r\n
\r\n \t
series<\/strong><\/dt>\r\n \t
the sum of the terms in a sequence<\/dd>\r\n<\/dl>\r\n
\r\n \t
set-builder notation<\/strong><\/dt>\r\n \t
a method of describing a set by a rule that all of its members obey; it takes the form [latex]\\left\\{x|\\text{statement about }x\\right\\}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
slope<\/strong><\/dt>\r\n \t
the change in\u00a0[latex]y[\/latex]<\/span>-<\/em>values over the change in\u00a0<\/span>[latex]x[\/latex]-<\/span>values<\/span><\/dd>\r\n<\/dl>\r\n
\r\n \t
slope-intercept form<\/strong><\/dt>\r\n \t
the equation of a linear function of the form [latex]f\\left(x\\right)=mx+b[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
solution set<\/strong><\/dt>\r\n \t
the set of all ordered pairs or triples that satisfy all equations in a system of equations<\/dd>\r\n<\/dl>\r\n
\r\n \t
square root property<\/strong><\/dt>\r\n \t
one of the methods used to solve a quadratic equation in which the [latex]{x}^{2}[\/latex] term is isolated so that the square root of both sides of the equation can be taken to solve for x<\/em><\/dd>\r\n<\/dl>\r\n
\r\n \t
standard form of a quadratic function<\/strong><\/dt>\r\n \t
the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex], where [latex]\\left(h,\\text{ }k\\right)[\/latex] is the vertex.<\/dd>\r\n<\/dl>\r\n
\r\n \t
substitution method<\/strong><\/dt>\r\n \t
An algebraic technique used to solve systems of linear equations in which one of the two equations is solved for one variable and then substituted into the second equation to solve for the second variable<\/dd>\r\n<\/dl>\r\n
\r\n \t
summation notation<\/strong><\/dt>\r\n \t
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series<\/dd>\r\n<\/dl>\r\n
\r\n \t
synthetic division<\/strong><\/dt>\r\n \t
a shortcut method that can be used to divide a polynomial by a binomial of the form [latex]x \u2013 k[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
system of linear equations<\/strong><\/dt>\r\n \t
A set of two or more equations in two or more variables that must be considered simultaneously<\/dd>\r\n<\/dl>\r\n
\r\n \t
term<\/strong><\/dt>\r\n \t
a number in a sequence<\/dd>\r\n<\/dl>\r\n
\r\n \t
term of a polynomial<\/strong><\/dt>\r\n \t
any [latex]{a}_{i}{x}^{i}[\/latex] of a polynomial of the form [latex]{a}_{n}{x}^{n}+\\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
term of a polynomial function<\/strong><\/dt>\r\n \t
any [latex]{a}_{i}{x}^{i}[\/latex]\u00a0of a polynomial function in the form [latex]f\\left(x\\right)={a}_{n}{x}^{n}+\\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
transverse Axis<\/strong><\/dt>\r\n \t
The axis of a hyperbola that includes the foci and has the vertices as its endpoints<\/dd>\r\n<\/dl>\r\n
\r\n \t
\r\n
\r\n \t
\r\n
\r\n \t
trinomial<\/strong><\/dt>\r\n \t
a polynomial containing three terms<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
turning point<\/strong><\/dt>\r\n \t
the location where the graph of a function changes direction<\/dd>\r\n<\/dl>\r\n
\r\n \t
union of two events<\/strong><\/dt>\r\n \t
the event that occurs if either or both events occur<\/dd>\r\n<\/dl>\r\n
\r\n \t
upper limit of summation<\/strong><\/dt>\r\n \t
the number used in the explicit formula to find the last term in a series<\/dd>\r\n<\/dl>\r\n
\r\n \t
variable<\/strong><\/dt>\r\n \t
a quantity that may change value<\/dd>\r\n<\/dl>\r\n
\r\n \t
varies directly<\/strong><\/dt>\r\n \t
a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\r\n<\/dl>\r\n
\r\n \t
varies inversely<\/strong><\/dt>\r\n \t
a relationship where one quantity is a constant divided by the other quantity<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertex<\/strong><\/dt>\r\n \t
The highest or lowest point of a parabola [latex](h,k)[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical asymptote<\/strong><\/dt>\r\n \t
a vertical line [latex]x=a[\/latex] where the graph tends toward positive or negative infinity as the inputs approach [latex]a[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical compression<\/strong><\/dt>\r\n \t
a function transformation that compresses the function\u2019s graph vertically by multiplying the output by a constant [latex]0<a<1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical line<\/strong><\/dt>\r\n \t
a line defined by [latex]x=a[\/latex] where a<\/em>\u00a0is a real number. The slope of a vertical line is undefined.<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical line test<\/strong><\/dt>\r\n \t
a method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical reflection<\/strong><\/dt>\r\n \t
a transformation that reflects a function\u2019s graph across the x<\/em>-axis by multiplying the output by [latex]-1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical shift<\/strong><\/dt>\r\n \t
a transformation that shifts a function\u2019s graph up or down by adding a positive or negative constant to the output<\/dd>\r\n<\/dl>\r\n
\r\n \t
vertical stretch<\/strong><\/dt>\r\n \t
a transformation that stretches a function\u2019s graph vertically by multiplying the output by a constant [latex]a>1[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
volume<\/strong><\/dt>\r\n \t
in cubic units, the volume measurement includes length, width, and depth: [latex]V=LWH[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
whole numbers<\/strong><\/dt>\r\n \t
the set consisting of [latex]0[\/latex] plus the natural numbers: [latex]\\{0,1,2,3,\\dots \\}[\/latex]<\/dd>\r\n<\/dl>\r\n
\r\n \t
x<\/em>-axis<\/strong><\/dt>\r\n \t
the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right<\/dd>\r\n<\/dl>\r\n
\r\n \t
x-<\/em>coordinate<\/strong><\/dt>\r\n \t
the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin<\/dd>\r\n<\/dl>\r\n
\r\n \t
x-<\/em>intercept<\/strong><\/dt>\r\n \t
the point where a graph intersects the x-<\/em>axis; an ordered pair with a y<\/em>-coordinate of zero<\/dd>\r\n<\/dl>\r\n
\r\n \t
y<\/em>-axis<\/strong><\/dt>\r\n \t
the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top<\/dd>\r\n<\/dl>\r\n
\r\n \t
y-<\/em>coordinate<\/strong><\/dt>\r\n \t
\u00a0the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin<\/dd>\r\n<\/dl>\r\n
\r\n \t
y<\/em>-intercept<\/strong><\/dt>\r\n \t
a point where a graph intercepts the y-<\/em>axis; an ordered pair with an x<\/em>-coordinate of zero<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n
\r\n \t
zero-product property<\/strong><\/dt>\r\n \t
the property that formally states that multiplication by zero is zero so that each factor of a quadratic equation can be set equal to zero to solve equations<\/dd>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>\r\n<\/dt>\r\n<\/dl>","rendered":"
\n
absolute maximum<\/strong><\/dt>\n
the greatest value of a function over an interval<\/dd>\n<\/dl>\n
\n
absolute minimum<\/strong><\/dt>\n
the lowest value of a function over an interval<\/dd>\n<\/dl>\n
\n
absolute value equation<\/strong><\/dt>\n
an equation in which the variable appears in absolute value bars, typically with two solutions, one accounting for the positive expression and one for the negative expression<\/dd>\n<\/dl>\n
\n
addition method<\/strong><\/dt>\n
An algebraic technique used to solve systems of linear equations in which the equations are added in a way that eliminates one variable, allowing the resulting equation to be solved for the remaining variable; substitution is then used to solve for the first variable<\/dd>\n<\/dl>\n
\n
addition principle<\/strong><\/dt>\n
if one event can occur in [latex]m[\/latex] ways and a second event with no common outcomes can occur in [latex]n[\/latex] ways, then the first or second event can occur in [latex]m+n[\/latex] ways<\/dd>\n<\/dl>\n
\n
algebraic expression<\/strong><\/dt>\n
constants and variables combined using addition, subtraction, multiplication, and division<\/dd>\n<\/dl>\n
\n
annual percentage rate (APR)<\/strong><\/dt>\n
the yearly interest rate earned by an investment account, also called nominal rate<\/em><\/dd>\n<\/dl>\n
\n
annuity<\/strong><\/dt>\n
an investment in which the purchaser makes a sequence of periodic, equal payments<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
area<\/strong><\/dt>\n
in square units, the area formula used in this section is used to find the area of any two-dimensional rectangular region: [latex]A=LW[\/latex]<\/dd>\n<\/dl>\n
\n
arithmetic sequence<\/strong><\/dt>\n
a sequence in which the difference between any two consecutive terms is a constant<\/dd>\n<\/dl>\n
\n
arithmetic series<\/strong><\/dt>\n
the sum of the terms in an arithmetic sequence<\/dd>\n<\/dl>\n
\n
arrow notation<\/strong><\/dt>\n
a way to symbolically represent the local and end behavior of a function by using arrows to indicate that an input or output approaches a value<\/dd>\n<\/dl>\n
\n
associative property of addition<\/strong><\/dt>\n
the sum of three numbers may be grouped differently without affecting the result; in symbols, [latex]a+\\left(b+c\\right)=\\left(a+b\\right)+c[\/latex]<\/dd>\n<\/dl>\n
\n
associative property of multiplication<\/strong><\/dt>\n
the product of three numbers may be grouped differently without affecting the result; in symbols, [latex]a\\cdot \\left(b\\cdot c\\right)=\\left(a\\cdot b\\right)\\cdot c[\/latex]<\/dd>\n<\/dl>\n
\n
augmented matrix<\/strong><\/dt>\n
a coefficient matrix adjoined with the constant column separated by a vertical line within the matrix brackets<\/dd>\n<\/dl>\n
\n
average rate of change<\/strong><\/dt>\n
the difference in the output values of a function found for two values of the input divided by the difference between the inputs<\/dd>\n<\/dl>\n
\n
axis of symmetry<\/strong><\/dt>\n
a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by [latex]x=-\\frac{b}{2a}[\/latex].<\/dd>\n<\/dl>\n
\n
base<\/strong><\/dt>\n
in exponential notation, [latex]a^n[\/latex] the expression that is being multiplied<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
binomial<\/strong><\/dt>\n
a polynomial containing two terms<\/dd>\n<\/dl>\n
\n
binomial coefficient<\/strong><\/dt>\n
the number of ways to choose [latex]r[\/latex] objects from [latex]n[\/latex]\u00a0objects where order does not matter; equivalent to [latex]C\\left(n,r\\right)[\/latex], denoted [latex]\\left(\\begin{gathered}n\\\\ r\\end{gathered}\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
binomial expansion<\/strong><\/dt>\n
the result of expanding [latex]{\\left(x+y\\right)}^{n}[\/latex] by multiplying<\/dd>\n<\/dl>\n
\n
binomial theorem<\/strong><\/dt>\n
a formula that can be used to expand any binomial<\/dd>\n<\/dl>\n
\n
break-even point<\/strong><\/dt>\n
The point at which a cost function intersects a revenue function; where profit is zero<\/dd>\n<\/dl>\n
\n
carrying capacity<\/strong><\/dt>\n
in a logistic model, the limiting value of the output<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
Cartesian coordinate system<\/strong><\/dt>\n
a grid system designed with perpendicular axes invented by Ren\u00e9 Descartes<\/dd>\n<\/dl>\n
\n
center of an Ellipse<\/strong><\/dt>\n
The midpoint of both the major and minor axes<\/dd>\n<\/dl>\n
\n
center of a Hyperbola<\/strong><\/dt>\n
The midpoint of both the transverse and conjugate axes of a hyperbola<\/dd>\n<\/dl>\n
\n
change-of-base formula<\/strong><\/dt>\n
a formula for converting a logarithm with any base to a quotient of logarithms with any other base<\/dd>\n<\/dl>\n
\n
coefficient<\/strong><\/dt>\n
any real number [latex]{a}_{i}[\/latex] in a polynomial of the form [latex]{a}_{n}{x}^{n}+\\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[\/latex]<\/dd>\n<\/dl>\n
\n
coefficient matrix<\/strong><\/dt>\n
a matrix that contains only the coefficients from a system of equations<\/dd>\n<\/dl>\n
\n
column<\/strong><\/dt>\n
a set of numbers aligned vertically in a matrix<\/dd>\n<\/dl>\n
\n
combination<\/strong><\/dt>\n
a selection of objects in which order does not matter<\/dd>\n<\/dl>\n
\n
common difference<\/strong><\/dt>\n
the difference between any two consecutive terms in an arithmetic sequence<\/dd>\n<\/dl>\n
\n
common logarithm<\/strong><\/dt>\n
the exponent to which [latex]10[\/latex] must be raised to get [latex]x[\/latex]; [latex]{\\mathrm{log}}_{10}\\left(x\\right)[\/latex] is written simply as [latex]\\mathrm{log}\\left(x\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
common ratio<\/strong><\/dt>\n
the ratio between any two consecutive terms in a geometric sequence<\/dd>\n<\/dl>\n
\n
commutative property of addition<\/strong><\/dt>\n
two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[\/latex]<\/dd>\n<\/dl>\n
\n
commutative property of multiplication<\/strong><\/dt>\n
two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\\cdot b=b\\cdot a[\/latex]<\/dd>\n<\/dl>\n
\n
complement of an event<\/strong><\/dt>\n
the set of outcomes in the sample space that are not in the event [latex]E[\/latex]<\/dd>\n<\/dl>\n
\n
completing the square<\/strong><\/dt>\n
a process for solving quadratic equations in which terms are added to or subtracted from both sides of the equation in order to make one side a perfect square<\/dd>\n<\/dl>\n
\n
complex conjugate<\/strong><\/dt>\n
the complex number in which the sign of the imaginary part is changed and the real part of the number is left unchanged; when added to or multiplied by the original complex number, the result is a real number<\/dd>\n<\/dl>\n
\n
complex number<\/strong><\/dt>\n
the sum of a real number and an imaginary number, written in the standard form [latex]a+bi[\/latex], where [latex]a[\/latex] is the real part, and [latex]bi[\/latex] is the imaginary part<\/dd>\n<\/dl>\n
\n
complex plane<\/strong><\/dt>\n
a coordinate system in which the horizontal axis is used to represent the real part of a complex number and the vertical axis is used to represent the imaginary part of a complex number<\/dd>\n<\/dl>\n
\n
complex roots<\/strong><\/dt>\n
Solutions to a quadratic equation that contain imaginary numbers, occurring when the discriminant is negative<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
composite function<\/strong><\/dt>\n
the new function formed by function composition, when the output of one function is used as the input of another<\/dd>\n<\/dl>\n
\n
compound inequality<\/strong><\/dt>\n
a problem or a statement that includes two inequalities<\/dd>\n<\/dl>\n
\n
compound interest<\/strong><\/dt>\n
interest earned on the total balance, not just the principal<\/dd>\n<\/dl>\n
\n
conic Section<\/strong><\/dt>\n
Any shape resulting from the intersection of a right circular cone with a plane<\/dd>\n<\/dl>\n
\n
conjugate Axis<\/strong><\/dt>\n
The axis of a hyperbola that is perpendicular to the transverse axis and has the co-vertices as its endpoints<\/dd>\n<\/dl>\n
\n
conjugate pair<\/strong><\/dt>\n
Two complex numbers in the form [latex]a + bi[\/latex] and [latex]a - bi[\/latex] that occur as solutions to quadratic equations with complex roots<\/dd>\n<\/dl>\n
\n
consistent system<\/strong><\/dt>\n
A system for which there is a single solution to all equations in the system and it is an independent system, or if there are an infinite number of solutions and it is a dependent system<\/dd>\n<\/dl>\n
\n
constant<\/strong><\/dt>\n
a quantity that does not change value<\/dd>\n<\/dl>\n
\n
constant of variation<\/strong><\/dt>\n
the non-zero value [latex]k[\/latex]\u00a0that helps define the relationship between variables in direct or inverse variation<\/dd>\n<\/dl>\n
\n
continuous function<\/strong><\/dt>\n
a function whose graph can be drawn without lifting the pen from the paper because there are no breaks in the graph<\/dd>\n<\/dl>\n
\n
cost function<\/strong><\/dt>\n
The function used to calculate the costs of doing business; it usually has two parts, fixed costs and variable costs<\/dd>\n<\/dl>\n
\n
correlation coefficient<\/strong><\/dt>\n
a value, [latex]r[\/latex], between [latex]\u20131[\/latex] and [latex]1[\/latex] that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.<\/dd>\n<\/dl>\n
\n
cross-multiplication<\/strong><\/dt>\n
A method for solving rational equations set up as a proportion by multiplying terms across the equal sign.<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
decreasing function<\/strong><\/dt>\n
a function is decreasing in some open interval if [latex]f\\left(b\\right)a[\/latex]<\/dd>\n<\/dl>\n
\n
decreasing linear function<\/strong><\/dt>\n
a function with a negative slope: If [latex]m<0, \\text{then }f\\left(x\\right)=mx+b[\/latex] is decreasing.<\/dd>\n<\/dl>\n
\n
degree<\/strong><\/dt>\n
the highest power of the variable that occurs in a polynomial<\/dd>\n<\/dl>\n
\n
dependent system<\/strong><\/dt>\n
A system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system<\/dd>\n<\/dl>\n
\n
dependent variable<\/strong><\/dt>\n
an output variable<\/dd>\n<\/dl>\n
\n
Descartes\u2019 Rule of Signs<\/strong><\/dt>\n
a rule that determines the maximum possible numbers of positive and negative real zeros based on the number of sign changes of [latex]f\\left(x\\right)[\/latex] and [latex]f\\left(-x\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
difference of squares<\/strong><\/dt>\n
the binomial that results when a binomial is multiplied by a binomial with the same terms, but the opposite sign<\/dd>\n<\/dl>\n
\n
direct variation<\/strong><\/dt>\n
the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other<\/dd>\n<\/dl>\n
\n
directrix<\/strong><\/dt>\n
a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic and the focus to the distance to the directrix is constant<\/dd>\n<\/dl>\n
\n
discriminant<\/strong><\/dt>\n
the value under the radical in the quadratic formula, [latex]b^2-4ac[\/latex], which tells whether the quadratic has real or complex roots<\/dd>\n<\/dl>\n
\n
distance formula<\/strong><\/dt>\n
a formula that can be used to find the length of a line segment if the endpoints are known<\/dd>\n<\/dl>\n
\n
<\/dt>\n<\/dl>\n
\n
distributive property<\/strong><\/dt>\n
the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, [latex]a\\cdot \\left(b+c\\right)=a\\cdot b+a\\cdot c[\/latex]<\/dd>\n<\/dl>\n
\n
Division Algorithm<\/strong><\/dt>\n
given a polynomial dividend [latex]f\\left(x\\right)[\/latex]\u00a0and a non-zero polynomial divisor [latex]d\\left(x\\right)[\/latex]\u00a0where the degree of [latex]d\\left(x\\right)[\/latex]\u00a0is less than or equal to the degree of [latex]f\\left(x\\right)[\/latex],\u00a0there exist unique polynomials [latex]q\\left(x\\right)[\/latex]\u00a0and [latex]r\\left(x\\right)[\/latex]\u00a0such that [latex]f\\left(x\\right)=d\\left(x\\right)q\\left(x\\right)+r\\left(x\\right)[\/latex]\u00a0where [latex]q\\left(x\\right)[\/latex]\u00a0is the quotient and [latex]r\\left(x\\right)[\/latex]\u00a0is the remainder. The remainder is either equal to zero or has degree strictly less than [latex]d\\left(x\\right)[\/latex].<\/dd>\n<\/dl>\n
\n
diverge<\/strong><\/dt>\n
a series is said to diverge if the sum is not a real number<\/dd>\n<\/dl>\n
\n
domain<\/strong><\/dt>\n
the set of all possible input values for a relation<\/dd>\n<\/dl>\n
\n
doubling time<\/strong><\/dt>\n
the time it takes for a quantity to double<\/dd>\n<\/dl>\n
\n
ellipse<\/strong><\/dt>\n
The set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the sum of their distances from two fixed points is a constant<\/dd>\n<\/dl>\n
\n
end behavior<\/strong><\/dt>\n
the behavior of the graph of a function as the input decreases without bound and increases without bound<\/dd>\n<\/dl>\n
\n
entry<\/strong><\/dt>\n
an element, coefficient, or constant in a matrix<\/dd>\n<\/dl>\n
\n
<\/dt>\n
equation<\/strong><\/dt>\n
a mathematical statement indicating that two expressions are equal<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
equation in two variables<\/strong><\/dt>\n
a mathematical statement, typically written in x <\/em>and y<\/em>, in which two expressions are equal<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
even function<\/strong><\/dt>\n
a function whose graph is unchanged by horizontal reflection, [latex]f\\left(x\\right)=f\\left(-x\\right)[\/latex], and is symmetric about the [latex]y\\text{-}[\/latex] axis<\/dd>\n<\/dl>\n
\n
event<\/strong><\/dt>\n
any subset of a sample space<\/dd>\n<\/dl>\n
\n
excluded values<\/strong><\/dt>\n
Values that make the denominator in a rational expression equal to zero, which must be excluded from the solution set.<\/dd>\n<\/dl>\n
\n
experiment<\/strong><\/dt>\n
an activity with an observable result<\/dd>\n<\/dl>\n
\n
explicit formula<\/strong><\/dt>\n
a formula that defines each term of a sequence in terms of its position in the sequence<\/dd>\n<\/dl>\n
\n
exponent<\/strong><\/dt>\n
in exponential notation, the raised number or variable that indicates how many times the base is being multiplied<\/dd>\n<\/dl>\n
\n
exponential growth<\/strong><\/dt>\n
a model that grows by a rate proportional to the amount present<\/dd>\n<\/dl>\n
\n
exponential notation<\/strong><\/dt>\n
a shorthand method of writing products of the same factor<\/dd>\n<\/dl>\n
\n
extraneous solution<\/strong><\/dt>\n
a solution introduced while solving an equation that does not satisfy the conditions of the original equation<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
extrapolation<\/strong><\/dt>\n
predicting a value outside the domain and range of the data<\/dd>\n<\/dl>\n
\n
factor by grouping<\/strong><\/dt>\n
a method for factoring a trinomial of the form [latex]a{x}^{2}+bx+c[\/latex] by dividing the x<\/em> term into the sum of two terms, factoring each portion of the expression separately, and then factoring out the GCF of the entire expression<\/dd>\n<\/dl>\n
\n
Factor Theorem<\/strong><\/dt>\n
k<\/em>\u00a0is a zero of polynomial function [latex]f\\left(x\\right)[\/latex] if and only if [latex]\\left(x-k\\right)[\/latex] \u00a0is a factor of [latex]f\\left(x\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
finite sequence<\/strong><\/dt>\n
a function whose domain consists of a finite subset of the positive integers [latex]\\left\\{1,2,\\dots n\\right\\}[\/latex] for some positive integer [latex]n[\/latex]<\/dd>\n<\/dl>\n
\n
focal diameter (latus rectum)<\/strong><\/dt>\n
the line segment that passes through the focus of a parabola parallel to the directrix, with endpoints on the parabola<\/dd>\n<\/dl>\n
\n
foci<\/strong><\/dt>\n
Plural of focus<\/dd>\n<\/dl>\n
\n
focus (of an ellipse)<\/strong><\/dt>\n
One of the two fixed points on the major axis of an ellipse such that the sum of the distances from these points to any point [latex]\\left(x,y\\right)[\/latex] on the ellipse is a constant<\/dd>\n<\/dl>\n
\n
focus (of a parabola)<\/strong><\/dt>\n
a fixed point in the interior of a parabola that lies on the axis of symmetry<\/dd>\n<\/dl>\n
\n
formula<\/strong><\/dt>\n
an equation expressing a relationship between constant and variable quantities<\/dd>\n<\/dl>\n
\n
function<\/strong><\/dt>\n
a relation in which each input value yields a unique output value<\/dd>\n<\/dl>\n
\n
fundamental counting principle<\/strong><\/dt>\n
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Multiplication Principle<\/dd>\n<\/dl>\n
\n
Fundamental Theorem of Algebra<\/strong><\/dt>\n
a polynomial function with degree greater than 0 has at least one complex zero<\/dd>\n<\/dl>\n
\n
Gaussian elimination<\/strong><\/dt>\n
using elementary row operations to obtain a matrix in row-echelon form<\/dd>\n<\/dl>\n
\n
general form of a quadratic function<\/strong><\/dt>\n
the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{x}^{2}+bx+c[\/latex], where [latex]a[\/latex], [latex]b[\/latex], and [latex]c[\/latex]\u00a0are real numbers and [latex]a\\ne 0[\/latex].<\/dd>\n<\/dl>\n
\n
geometric sequence<\/strong><\/dt>\n
a sequence in which the ratio of a term to a previous term is a constant<\/dd>\n<\/dl>\n
\n
geometric series<\/strong><\/dt>\n
the sum of the terms in a geometric sequence<\/dd>\n<\/dl>\n
\n
global maximum<\/strong><\/dt>\n
highest turning point on a graph; [latex]f\\left(a\\right)[\/latex]\u00a0where [latex]f\\left(a\\right)\\ge f\\left(x\\right)[\/latex]\u00a0for all [latex]x[\/latex].<\/dd>\n<\/dl>\n
\n
global minimum<\/b><\/dt>\n
lowest turning point on a graph; [latex]f\\left(a\\right)[\/latex]\u00a0where [latex]f\\left(a\\right)\\le f\\left(x\\right)[\/latex] for all [latex]x[\/latex].<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
graph in two variables<\/strong><\/dt>\n
the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane<\/dd>\n<\/dl>\n
\n
greatest common factor<\/strong><\/dt>\n
the largest polynomial that divides evenly into each polynomial<\/dd>\n<\/dl>\n
\n
half-life<\/strong><\/dt>\n
the length of time it takes for a substance to exponentially decay to half of its original quantity<\/dd>\n<\/dl>\n
\n
horizontal asymptote<\/strong><\/dt>\n
a horizontal line [latex]y=b[\/latex]\u00a0where the graph approaches the line as the inputs increase or decrease without bound.<\/dd>\n<\/dl>\n
\n
horizontal compression<\/strong><\/dt>\n
a transformation that compresses a function\u2019s graph horizontally, by multiplying the input by a constant [latex]b>1[\/latex]<\/dd>\n<\/dl>\n
\n
horizontal line<\/strong><\/dt>\n
a line defined by [latex]f\\left(x\\right)=b[\/latex] where [latex]b[\/latex] is a real number. The slope of a horizontal line is [latex]0[\/latex].<\/dd>\n<\/dl>\n
\n
horizontal line test<\/strong><\/dt>\n
a method of testing whether a function is one-to-one by determining whether any horizontal line intersects the graph more than once<\/dd>\n<\/dl>\n
\n
horizontal reflection<\/strong><\/dt>\n
a transformation that reflects a function\u2019s graph across the y<\/em>-axis by multiplying the input by [latex]-1[\/latex]<\/dd>\n<\/dl>\n
\n
horizontal shift<\/strong><\/dt>\n
a transformation that shifts a function\u2019s graph left or right by adding a positive or negative constant to the input<\/dd>\n<\/dl>\n
\n
horizontal stretch<\/strong><\/dt>\n
a transformation that stretches a function\u2019s graph horizontally by multiplying the input by a constant [latex]0\n<\/dl>\n
\n
hyperbola<\/strong><\/dt>\n
The set of all points [latex]\\left(x,y\\right)[\/latex] in a plane such that the difference of the distances between [latex]\\left(x,y\\right)[\/latex] and the foci is a positive constant<\/dd>\n<\/dl>\n
\n
identity matrix<\/strong><\/dt>\n
a square matrix containing ones down the main diagonal and zeros everywhere else; it acts as a 1 in matrix algebra<\/dd>\n<\/dl>\n
\n
identity property of addition<\/strong><\/dt>\n
there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, [latex]a+0=a[\/latex]<\/dd>\n<\/dl>\n
\n
identity property of multiplication<\/strong><\/dt>\n
there is a unique number, called the multiplicative identity, [latex]1[\/latex], which, when multiplied by a number, results in the original number; in symbols, [latex]a\\cdot 1=a[\/latex]<\/dd>\n<\/dl>\n
\n
imaginary number<\/strong><\/dt>\n
a number in the form [latex]bi[\/latex]\u00a0where [latex]i=\\sqrt{-1}[\/latex]<\/dd>\n<\/dl>\n
\n
inconsistent system<\/strong><\/dt>\n
A system of linear equations with no common solution because they represent parallel lines, which have no point or line in common<\/dd>\n<\/dl>\n
\n
increasing function<\/strong><\/dt>\n
a function is increasing in some open interval if [latex]f\\left(b\\right)>f\\left(a\\right)[\/latex] for any two input values [latex]a[\/latex] and [latex]b[\/latex] in the given interval where [latex]b>a[\/latex]<\/dd>\n<\/dl>\n
\n
increasing linear function<\/strong><\/dt>\n
a function with a positive slope: If [latex]m>0, \\text{then }f\\left(x\\right)=mx+b[\/latex] is increasing.<\/dd>\n<\/dl>\n
\n
independent system<\/strong><\/dt>\n
A system of linear equations with exactly one solution pair [latex]\\left(x,y\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
independent variable<\/strong><\/dt>\n
an input variable<\/dd>\n<\/dl>\n
\n
index<\/strong><\/dt>\n
the number above the radical sign indicating the n<\/em>th root<\/dd>\n<\/dl>\n
\n
index of summation<\/strong><\/dt>\n
in summation notation, the variable used in the explicit formula for the terms of a series and written below the sigma with the lower limit of summation<\/dd>\n<\/dl>\n
\n
infinite sequence<\/strong><\/dt>\n
a function whose domain is the set of positive integers<\/dd>\n<\/dl>\n
\n
infinite series<\/strong><\/dt>\n
the sum of the terms in an infinite sequence<\/dd>\n<\/dl>\n
\n
input<\/strong><\/dt>\n
each object or value in a domain that relates to another object or value by a relationship known as a function<\/dd>\n<\/dl>\n
\n
integers<\/strong><\/dt>\n
the set consisting of the natural numbers, their opposites, and [latex]0[\/latex]: [latex]\\{\\dots ,-3,-2,-1,0,1,2,3,\\dots \\}[\/latex]<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
<\/dd>\n<\/dl>\n
\n
intercepts<\/strong><\/dt>\n
the points at which the graph of an equation crosses the x<\/em>-axis and the y<\/em>-axis<\/dd>\n<\/dl>\n
\n
Intermediate Value Theorem<\/strong><\/dt>\n
for two numbers [latex]a[\/latex]\u00a0and [latex]b[\/latex]\u00a0in the domain of [latex]f[\/latex],\u00a0if [latex]a\n<\/dl>\n
\n
interpolation<\/strong><\/dt>\n
predicting a value inside the domain and range of the data<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
interval<\/strong><\/dt>\n
an interval describes a set of numbers where a solution falls<\/dd>\n<\/dl>\n
\n
interval notation<\/strong><\/dt>\n
a mathematical statement that describes a solution set and uses parentheses or brackets to indicate where an interval begins and ends<\/dd>\n<\/dl>\n
\n
inverse function<\/strong><\/dt>\n
for any one-to-one function [latex]f\\left(x\\right)[\/latex], the inverse is a function [latex]{f}^{-1}\\left(x\\right)[\/latex] such that [latex]{f}^{-1}\\left(f\\left(x\\right)\\right)=x[\/latex] for all [latex]x[\/latex] in the domain of [latex]f[\/latex]; this also implies that [latex]f\\left({f}^{-1}\\left(x\\right)\\right)=x[\/latex] for all [latex]x[\/latex] in the domain of [latex]{f}^{-1}[\/latex]<\/dd>\n<\/dl>\n
\n
inverse property of addition<\/strong><\/dt>\n
for every real number [latex]a[\/latex], there is a unique number, called the additive inverse (or opposite), denoted [latex]-a[\/latex], which, when added to the original number, results in the additive identity, 0; in symbols, [latex]a+\\left(-a\\right)=0[\/latex]<\/dd>\n<\/dl>\n
\n
inverse property of multiplication<\/strong><\/dt>\n
for every non-zero real number [latex]a[\/latex], there is a unique number, called the multiplicative inverse (or reciprocal), denoted [latex]\\dfrac{1}{a}[\/latex], which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, [latex]a\\cdot \\dfrac{1}{a}=1[\/latex]<\/dd>\n<\/dl>\n
\n
inverse variation<\/strong><\/dt>\n
the relationship between two variables in which the product of the variables is a constant<\/dd>\n<\/dl>\n
\n
inversely proportional<\/strong><\/dt>\n
a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases<\/dd>\n<\/dl>\n
\n
invertible function<\/strong><\/dt>\n
any function that has an inverse function<\/dd>\n<\/dl>\n
\n
irrational numbers<\/strong><\/dt>\n
the set of all numbers that are not rational; they cannot be written as either a terminating or repeating decimal; they cannot be expressed as a fraction of two integers<\/dd>\n<\/dl>\n
\n
joint variation<\/strong><\/dt>\n
a relationship where a variable varies directly or inversely with multiple variables<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
leading coefficient<\/strong><\/dt>\n
the coefficient of the leading term<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
leading term<\/strong><\/dt>\n
\u00a0the term containing the highest degree<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
least common denominator<\/strong><\/dt>\n
the smallest multiple that two denominators have in common<\/dd>\n<\/dl>\n
\n
least squares regression<\/strong><\/dt>\n
a statistical technique for fitting a line to data in a way that minimizes the differences between the line and data values<\/dd>\n<\/dl>\n
\n
Linear Factorization Theorem<\/strong><\/dt>\n<\/dl>\n
\n
allowing for multiplicities, a polynomial function will have the same number of factors as its degree, and each factor will be in the form [latex]\\left(x-c\\right)[\/latex] where c<\/em>\u00a0is a complex number<\/dd>\n<\/dl>\n
\n
linear function<\/strong><\/dt>\n
a function with a constant rate of change that is a polynomial of degree [latex]1[\/latex] whose graph is a straight line<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
linear inequality<\/strong><\/dt>\n
similar to a linear equation except that the solutions will include an interval of numbers<\/dd>\n<\/dl>\n
\n
local extrema<\/strong><\/dt>\n
collectively, all of a function’s local maxima and minima<\/dd>\n<\/dl>\n
\n
local maximum<\/strong><\/dt>\n
a value of the input where a function changes from increasing to decreasing as the input value increases.<\/dd>\n<\/dl>\n
\n
local minimum<\/strong><\/dt>\n
a value of the input where a function changes from decreasing to increasing as the input value increases.<\/dd>\n<\/dl>\n
\n
logarithm<\/strong><\/dt>\n
the exponent to which [latex]b[\/latex]\u00a0must be raised to get [latex]x[\/latex]; written [latex]y={\\mathrm{log}}_{b}\\left(x\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
logistic growth model<\/strong><\/dt>\n
a function of the form [latex]f\\left(x\\right)=\\frac{c}{1+a{e}^{-bx}}[\/latex] where [latex]\\frac{c}{1+a}[\/latex] is the initial value, c<\/em>\u00a0is the carrying capacity, or limiting value, and b<\/em>\u00a0is a constant determined by the rate of growth<\/dd>\n<\/dl>\n
\n
lower limit of summation<\/strong><\/dt>\n
the number used in the explicit formula to find the first term in a series<\/dd>\n<\/dl>\n
\n
main diagonal<\/strong><\/dt>\n
entries from the upper left corner diagonally to the lower right corner of a square matrix<\/dd>\n<\/dl>\n
\n
major Axis<\/strong><\/dt>\n
The longer of the two axes of an ellipse<\/dd>\n<\/dl>\n
\n
matrix<\/strong><\/dt>\n
a rectangular array of numbers<\/dd>\n<\/dl>\n
\n
midpoint formula<\/strong><\/dt>\n
\u00a0a formula to find the point that divides a line segment into two parts of equal length<\/dd>\n<\/dl>\n
\n
minor Axis<\/strong><\/dt>\n
The shorter of the two axes of an ellipse<\/dd>\n<\/dl>\n
\n
model breakdown<\/strong><\/dt>\n
when a model no longer applies after a certain point<\/dd>\n<\/dl>\n
\n
monomial<\/strong><\/dt>\n
a polynomial containing one term<\/dd>\n<\/dl>\n
\n
multiplication principle<\/strong><\/dt>\n
if one event can occur in [latex]m[\/latex] ways and a second event can occur in [latex]n[\/latex] ways after the first event has occurred, then the two events can occur in [latex]m\\times n[\/latex] ways; also known as the Fundamental Counting Principle<\/dd>\n<\/dl>\n
\n
multiplicative inverse of a matrix<\/strong><\/dt>\n
a matrix that, when multiplied by the original, equals the identity matrix<\/dd>\n<\/dl>\n
\n
multiplicity<\/strong><\/dt>\n
the number of times a given factor appears in the factored form of the equation of a polynomial; if a polynomial contains a factor of the form [latex]{\\left(x-h\\right)}^{p}[\/latex], [latex]x=h[\/latex]\u00a0is a zero of multiplicity [latex]p[\/latex].<\/dd>\n<\/dl>\n
\n
mutually exclusive events<\/strong><\/dt>\n
events that have no outcomes in common<\/dd>\n<\/dl>\n
\n
natural logarithm<\/strong><\/dt>\n
the exponent to which the number [latex]e[\/latex]\u00a0must be raised to get [latex]x[\/latex]; [latex]{\\mathrm{log}}_{e}\\left(x\\right)[\/latex] is written as [latex]\\mathrm{ln}\\left(x\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
natural numbers<\/strong><\/dt>\n
the set of counting numbers: [latex]\\{1,2,3,\\dots \\}[\/latex]<\/dd>\n<\/dl>\n
\n
Newton\u2019s Law of Cooling<\/strong><\/dt>\n
the scientific formula for temperature as a function of time as an object\u2019s temperature is equalized with the ambient temperature<\/dd>\n<\/dl>\n
\n
[latex]n[\/latex] factorial<\/strong><\/dt>\n
the product of all the positive integers from 1 to [latex]n[\/latex]<\/dd>\n<\/dl>\n
\n
nominal rate<\/strong><\/dt>\n
the yearly interest rate earned by an investment account, also called annual percentage rate<\/em><\/dd>\n<\/dl>\n
\n
[latex]n[\/latex]th partial sum<\/strong><\/dt>\n
the sum of the first [latex]n[\/latex] terms of a sequence<\/dd>\n<\/dl>\n
\n
[latex]n[\/latex]th term of a sequence<\/strong><\/dt>\n
a formula for the general term of a sequence<\/dd>\n<\/dl>\n
\n
odd function<\/strong><\/dt>\n
a function whose graph is unchanged by combined horizontal and vertical reflection, [latex]f\\left(x\\right)=-f\\left(-x\\right)[\/latex], and is symmetric about the origin<\/dd>\n<\/dl>\n
\n
one-to-one function<\/strong><\/dt>\n
a function for which each value of the output is associated with a unique input value<\/dd>\n<\/dl>\n
\n
order of magnitude<\/strong><\/dt>\n
the power of ten when a number is expressed in scientific notation with one non-zero digit to the left of the decimal<\/dd>\n<\/dl>\n
\n
order of operations<\/strong><\/dt>\n
a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
\n<\/dt>\n
ordered pair<\/strong><\/dt>\n
a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, [latex]\\left(x,y\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
origin<\/strong><\/dt>\n
the point where the two axes cross in the center of the plane, described by the ordered pair [latex]\\left(0,0\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
outcomes<\/strong><\/dt>\n
the possible results of an experiment<\/dd>\n<\/dl>\n
\n
output<\/strong><\/dt>\n
each object or value in the range that is produced when an input value is entered into a function<\/dd>\n<\/dl>\n
\n
parabola<\/strong><\/dt>\n
the set of all points [latex]\\left(x,y\\right)[\/latex] in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix<\/dd>\n<\/dl>\n
\n
parallel lines<\/strong><\/dt>\n
two or more lines with the same slope<\/dd>\n<\/dl>\n
\n
partial fractions<\/strong><\/dt>\n
\u00a0the individual fractions that make up the sum or difference of a rational expression before combining them into a simplified rational expression<\/dd>\n<\/dl>\n
\n
partial fraction decomposition<\/strong><\/dt>\n
the process of returning a simplified rational expression to its original form, a sum or difference of simpler rational expressions<\/dd>\n<\/dl>\n
\n
perfect square trinomial<\/strong><\/dt>\n
the trinomial that results when a binomial is squared<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
\n<\/dt>\n
perimeter<\/strong><\/dt>\n
in linear units, the perimeter formula is used to find the linear measurement, or outside length and width, around a two-dimensional regular object; for a rectangle: [latex]P=2L+2W[\/latex]<\/dd>\n<\/dl>\n
\n
permutation<\/strong><\/dt>\n
a selection of objects in which order matters<\/dd>\n<\/dl>\n
\n
perpendicular lines<\/strong><\/dt>\n
two lines that intersect at right angles and have slopes that are negative reciprocals of each other<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
piecewise function<\/strong><\/dt>\n
a function in which more than one formula is used to define the output<\/dd>\n<\/dl>\n
\n
point-slope form<\/strong><\/dt>\n
the equation of a linear function of the form [latex]y-{y}_{1}=m\\left(x-{x}_{1}\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
polynomial<\/strong><\/dt>\n
a sum of terms each consisting of a variable raised to a nonnegative integer power<\/dd>\n<\/dl>\n
\n
polynomial function<\/strong><\/dt>\n
a function that consists of either zero or the sum of a finite number of non-zero\u00a0terms, each of which is a product of a number, called the\u00a0coefficient\u00a0of the term, and a variable raised to a non-negative integer power.<\/dd>\n<\/dl>\n
\n
polynomial equation<\/strong><\/dt>\n
an equation containing a string of terms including numerical coefficients and variables raised to whole-number exponents<\/dd>\n<\/dl>\n
\n
power function<\/strong><\/dt>\n
a function that can be represented in the form [latex]f\\left(x\\right)=a{x}^{n}[\/latex]\u00a0where a\u00a0<\/em>is a constant, the base is a variable, and the exponent is\u00a0n<\/i>,\u00a0is a smooth curve represented by a graph with no sharp corners<\/dd>\n<\/dl>\n
\n
power rule for logarithms<\/strong><\/dt>\n
a rule of logarithms that states that the log of a power is equal to the product of the exponent and the log of its base<\/dd>\n<\/dl>\n
\n
principal n<\/em>th root<\/strong><\/dt>\n
the number with the same sign as [latex]a[\/latex] that when raised to the n<\/em>th power equals [latex]a[\/latex]<\/dd>\n<\/dl>\n
\n
principal square root<\/strong><\/dt>\n
the nonnegative square root of a number [latex]a[\/latex] that, when multiplied by itself, equals [latex]a[\/latex]<\/dd>\n<\/dl>\n
\n
probability<\/strong><\/dt>\n
a number from [latex]0[\/latex] to [latex]1[\/latex] indicating the likelihood of an event<\/dd>\n<\/dl>\n
\n
probability model<\/strong><\/dt>\n
a mathematical description of an experiment listing all possible outcomes and their associated probabilities<\/dd>\n<\/dl>\n
\n
product rule for logarithms<\/strong><\/dt>\n
a rule of logarithms that states that the log of a product is equal to a sum of logarithms<\/dd>\n<\/dl>\n
\n
profit function<\/strong><\/dt>\n
The profit function is written as [latex]P\\left(x\\right)=R\\left(x\\right)-C\\left(x\\right)[\/latex], revenue minus cost<\/dd>\n<\/dl>\n
\n
projectile motion<\/strong><\/dt>\n
motion of an object thrown or launched near Earth’s surface<\/dd>\n<\/dl>\n
\n
Pythagorean Theorem<\/strong><\/dt>\n
a theorem that states the relationship among the lengths of the sides of a right triangle, used to solve right triangle problems<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
quadrant<\/strong><\/dt>\n
one quarter of the coordinate plane, created when the axes divide the plane into four sections<\/dd>\n<\/dl>\n
\n
quadratic equation<\/strong><\/dt>\n
an equation containing a second-degree polynomial; can be solved using multiple methods<\/dd>\n<\/dl>\n
\n
quadratic formula<\/strong><\/dt>\n
a formula that will solve all quadratic equations<\/dd>\n<\/dl>\n
\n
quadratic function<\/strong><\/dt>\n
A polynomial function of degree 2<\/dd>\n<\/dl>\n
\n
quotient rule for logarithms<\/strong><\/dt>\n
a rule of logarithms that states that the log of a quotient is equal to a difference of logarithms<\/dd>\n<\/dl>\n
\n
radical<\/strong><\/dt>\n
the symbol used to indicate a root<\/dd>\n<\/dl>\n
\n
radical equation<\/strong><\/dt>\n
an equation containing at least one radical term where the variable is part of the radicand<\/dd>\n<\/dl>\n
\n
radical expression<\/strong><\/dt>\n
an expression containing a radical symbol<\/dd>\n<\/dl>\n
\n
radicand<\/strong><\/dt>\n
the number under the radical symbol<\/dd>\n<\/dl>\n
\n
range<\/strong><\/dt>\n
the set of output values that result from the input values in a relation<\/dd>\n<\/dl>\n
\n
rate<\/strong><\/dt>\n
speed or frequency at which something occurs<\/dd>\n<\/dl>\n
\n
rate of change<\/strong><\/dt>\n
the change of an output quantity relative to the change of the input quantity<\/dd>\n<\/dl>\n
\n
rational equation<\/strong><\/dt>\n
An equation that contains at least one rational expression, where the variable appears in at least one of the denominators.<\/dd>\n<\/dl>\n
\n
rational expression<\/strong><\/dt>\n
The ratio or quotient of two polynomials, e.g., \\( \\frac{x+1}{x^2-4} \\), \\( \\frac{1}{x-3} \\), or \\( \\frac{4}{x^2+x-2} \\).<\/dd>\n<\/dl>\n
\n
rational function<\/strong><\/dt>\n
a function that can be written as the ratio of two polynomials<\/dd>\n<\/dl>\n
\n
rational numbers<\/strong><\/dt>\n
the set of all numbers of the form [latex]\\dfrac{m}{n}[\/latex], where [latex]m[\/latex] and [latex]n[\/latex] are integers and [latex]n\\ne 0[\/latex]. Any rational number may be written as a fraction or a terminating or repeating decimal.<\/dd>\n<\/dl>\n
\n
Rational Zero Theorem<\/strong><\/dt>\n
the possible rational zeros of a polynomial function have the form [latex]\\frac{p}{q}[\/latex] where p<\/em>\u00a0is a factor of the constant term and q<\/em>\u00a0is a factor of the leading coefficient<\/dd>\n<\/dl>\n
\n
real number line<\/strong><\/dt>\n
a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.<\/dd>\n<\/dl>\n
\n
real numbers<\/strong><\/dt>\n
the sets of rational numbers and irrational numbers taken together<\/dd>\n<\/dl>\n
\n
recursive formula<\/strong><\/dt>\n
a formula that defines each term of a sequence using previous term(s)<\/dd>\n<\/dl>\n
\n
relation<\/strong><\/dt>\n
a set of ordered pairs<\/dd>\n<\/dl>\n
\n
Remainder Theorem<\/strong><\/dt>\n
if a polynomial [latex]f\\left(x\\right)[\/latex] is divided by [latex]x-k[\/latex] , then the remainder is equal to the value [latex]f\\left(k\\right)[\/latex]<\/dd>\n<\/dl>\n
\n
removable discontinuity<\/strong><\/dt>\n
a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function<\/dd>\n<\/dl>\n
\n
revenue function<\/strong><\/dt>\n
The function that is used to calculate revenue, simply written as [latex]R=xp[\/latex], where [latex]x=[\/latex] quantity and [latex]p=[\/latex] price<\/dd>\n<\/dl>\n
\n
row<\/strong><\/dt>\n
a set of numbers aligned horizontally in a matrix<\/dd>\n<\/dl>\n
\n
row-echelon form<\/strong><\/dt>\n
after performing row operations, the matrix form that contains ones down the main diagonal and zeros at every space below the diagonal<\/dd>\n<\/dl>\n
\n
row-equivalent<\/strong><\/dt>\n
two matrices [latex]A[\/latex] and [latex]B[\/latex] are row-equivalent if one can be obtained from the other by performing basic row operations<\/dd>\n<\/dl>\n
\n
row operations<\/strong><\/dt>\n
adding one row to another row, multiplying a row by a constant, interchanging rows, and so on, with the goal of achieving row-echelon form<\/dd>\n<\/dl>\n
\n
sample space<\/strong><\/dt>\n
the set of all possible outcomes of an experiment<\/dd>\n<\/dl>\n
\n
scalar multiple<\/strong><\/dt>\n
an entry of a matrix that has been multiplied by a scalar<\/dd>\n<\/dl>\n
\n
scientific notation<\/strong><\/dt>\n
a shorthand notation for writing very large or very small numbers in the form [latex]a\\times {10}^{n}[\/latex] where [latex]1\\le |a|<10[\/latex] and [latex]n[\/latex] is an integer<\/dd>\n<\/dl>\n
\n
sequence<\/strong><\/dt>\n
a function whose domain is a subset of the positive integers<\/dd>\n<\/dl>\n
\n
series<\/strong><\/dt>\n
the sum of the terms in a sequence<\/dd>\n<\/dl>\n
\n
set-builder notation<\/strong><\/dt>\n
a method of describing a set by a rule that all of its members obey; it takes the form [latex]\\left\\{x|\\text{statement about }x\\right\\}[\/latex]<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
\n<\/dt>\n
\n<\/dt>\n
slope<\/strong><\/dt>\n
the change in\u00a0[latex]y[\/latex]<\/span>–<\/em>values over the change in\u00a0<\/span>[latex]x[\/latex]–<\/span>values<\/span><\/dd>\n<\/dl>\n
\n
slope-intercept form<\/strong><\/dt>\n
the equation of a linear function of the form [latex]f\\left(x\\right)=mx+b[\/latex]<\/dd>\n<\/dl>\n
\n
solution set<\/strong><\/dt>\n
the set of all ordered pairs or triples that satisfy all equations in a system of equations<\/dd>\n<\/dl>\n
\n
square root property<\/strong><\/dt>\n
one of the methods used to solve a quadratic equation in which the [latex]{x}^{2}[\/latex] term is isolated so that the square root of both sides of the equation can be taken to solve for x<\/em><\/dd>\n<\/dl>\n
\n
standard form of a quadratic function<\/strong><\/dt>\n
the function that describes a parabola, written in the form [latex]f\\left(x\\right)=a{\\left(x-h\\right)}^{2}+k[\/latex], where [latex]\\left(h,\\text{ }k\\right)[\/latex] is the vertex.<\/dd>\n<\/dl>\n
\n
substitution method<\/strong><\/dt>\n
An algebraic technique used to solve systems of linear equations in which one of the two equations is solved for one variable and then substituted into the second equation to solve for the second variable<\/dd>\n<\/dl>\n
\n
summation notation<\/strong><\/dt>\n
a notation for series using the Greek letter sigma; it includes an explicit formula and specifies the first and last terms in the series<\/dd>\n<\/dl>\n
\n
synthetic division<\/strong><\/dt>\n
a shortcut method that can be used to divide a polynomial by a binomial of the form [latex]x \u2013 k[\/latex]<\/dd>\n<\/dl>\n
\n
system of linear equations<\/strong><\/dt>\n
A set of two or more equations in two or more variables that must be considered simultaneously<\/dd>\n<\/dl>\n
\n
term<\/strong><\/dt>\n
a number in a sequence<\/dd>\n<\/dl>\n
\n
term of a polynomial<\/strong><\/dt>\n
any [latex]{a}_{i}{x}^{i}[\/latex] of a polynomial of the form [latex]{a}_{n}{x}^{n}+\\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[\/latex]<\/dd>\n<\/dl>\n
\n
term of a polynomial function<\/strong><\/dt>\n
any [latex]{a}_{i}{x}^{i}[\/latex]\u00a0of a polynomial function in the form [latex]f\\left(x\\right)={a}_{n}{x}^{n}+\\dots+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}[\/latex]<\/dd>\n<\/dl>\n
\n
transverse Axis<\/strong><\/dt>\n
The axis of a hyperbola that includes the foci and has the vertices as its endpoints<\/dd>\n<\/dl>\n
\n
\n<\/dt>\n
\n<\/dt>\n
trinomial<\/strong><\/dt>\n
a polynomial containing three terms<\/dd>\n<\/dl>\n
\n
turning point<\/strong><\/dt>\n
the location where the graph of a function changes direction<\/dd>\n<\/dl>\n
\n
union of two events<\/strong><\/dt>\n
the event that occurs if either or both events occur<\/dd>\n<\/dl>\n
\n
upper limit of summation<\/strong><\/dt>\n
the number used in the explicit formula to find the last term in a series<\/dd>\n<\/dl>\n
\n
variable<\/strong><\/dt>\n
a quantity that may change value<\/dd>\n<\/dl>\n
\n
varies directly<\/strong><\/dt>\n
a relationship where one quantity is a constant multiplied by the other quantity<\/dd>\n<\/dl>\n
\n
varies inversely<\/strong><\/dt>\n
a relationship where one quantity is a constant divided by the other quantity<\/dd>\n<\/dl>\n
\n
vertex<\/strong><\/dt>\n
The highest or lowest point of a parabola [latex](h,k)[\/latex]<\/dd>\n<\/dl>\n
\n
vertical asymptote<\/strong><\/dt>\n
a vertical line [latex]x=a[\/latex] where the graph tends toward positive or negative infinity as the inputs approach [latex]a[\/latex]<\/dd>\n<\/dl>\n
\n
vertical compression<\/strong><\/dt>\n
a function transformation that compresses the function\u2019s graph vertically by multiplying the output by a constant [latex]0\n<\/dl>\n
\n
vertical line<\/strong><\/dt>\n
a line defined by [latex]x=a[\/latex] where a<\/em>\u00a0is a real number. The slope of a vertical line is undefined.<\/dd>\n<\/dl>\n
\n
vertical line test<\/strong><\/dt>\n
a method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once<\/dd>\n<\/dl>\n
\n
vertical reflection<\/strong><\/dt>\n
a transformation that reflects a function\u2019s graph across the x<\/em>-axis by multiplying the output by [latex]-1[\/latex]<\/dd>\n<\/dl>\n
\n
vertical shift<\/strong><\/dt>\n
a transformation that shifts a function\u2019s graph up or down by adding a positive or negative constant to the output<\/dd>\n<\/dl>\n
\n
vertical stretch<\/strong><\/dt>\n
a transformation that stretches a function\u2019s graph vertically by multiplying the output by a constant [latex]a>1[\/latex]<\/dd>\n<\/dl>\n
\n
volume<\/strong><\/dt>\n
in cubic units, the volume measurement includes length, width, and depth: [latex]V=LWH[\/latex]<\/dd>\n<\/dl>\n
\n
whole numbers<\/strong><\/dt>\n
the set consisting of [latex]0[\/latex] plus the natural numbers: [latex]\\{0,1,2,3,\\dots \\}[\/latex]<\/dd>\n<\/dl>\n
\n
x<\/em>-axis<\/strong><\/dt>\n
the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right<\/dd>\n<\/dl>\n
\n
x-<\/em>coordinate<\/strong><\/dt>\n
the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin<\/dd>\n<\/dl>\n
\n
x-<\/em>intercept<\/strong><\/dt>\n
the point where a graph intersects the x-<\/em>axis; an ordered pair with a y<\/em>-coordinate of zero<\/dd>\n<\/dl>\n
\n
y<\/em>-axis<\/strong><\/dt>\n
the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top<\/dd>\n<\/dl>\n
\n
y-<\/em>coordinate<\/strong><\/dt>\n
\u00a0the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin<\/dd>\n<\/dl>\n
\n
y<\/em>-intercept<\/strong><\/dt>\n
a point where a graph intercepts the y-<\/em>axis; an ordered pair with an x<\/em>-coordinate of zero<\/dd>\n<\/dl>\n
\n
zero-product property<\/strong><\/dt>\n
the property that formally states that multiplication by zero is zero so that each factor of a quadratic equation can be set equal to zero to solve equations<\/dd>\n<\/dl>\n","protected":false},"author":15,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":21,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5567"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":29,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5567\/revisions"}],"predecessor-version":[{"id":7380,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5567\/revisions\/7380"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/21"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/5567\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=5567"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=5567"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=5567"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=5567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}