{"id":148,"date":"2026-01-12T15:55:06","date_gmt":"2026-01-12T15:55:06","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&#038;p=148"},"modified":"2026-01-12T15:55:06","modified_gmt":"2026-01-12T15:55:06","slug":"basic-functions-and-graphs-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/basic-functions-and-graphs-get-stronger-answer-key\/","title":{"raw":"Basic Functions and Graphs: Get Stronger Answer Key","rendered":"Basic Functions and Graphs: Get Stronger Answer Key"},"content":{"raw":"<h2 class=\"entry-title\">Review of Functions<\/h2>\r\n<ol style=\"list-style-type: decimal;\">\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain = [latex]\\{-3,-2,-1,0,1,2,3\\}[\/latex], range = [latex]\\{0,1,4,9\\}[\/latex]<\/li>\r\n \t<li>Yes, a function<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain = [latex]\\{0,1,2,3\\}[\/latex], range = [latex]\\{-3,-2,-1,0,1,2,3\\}[\/latex]<\/li>\r\n \t<li>No, not a function<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain = [latex]\\{3,5,8,10,15,21,33\\}[\/latex], range = [latex]\\{0,1,2,3\\}[\/latex]<\/li>\r\n \t<li>Yes, a function<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]-2[\/latex]<\/li>\r\n \t<li>[latex]3[\/latex]<\/li>\r\n \t<li>[latex]13[\/latex]<\/li>\r\n \t<li>[latex]-5x-2[\/latex]<\/li>\r\n \t<li>[latex]5a-2[\/latex]<\/li>\r\n \t<li>[latex]5a+5h-2[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Undefined<\/li>\r\n \t<li>[latex]2[\/latex]<\/li>\r\n \t<li>[latex]\\frac{2}{3}[\/latex]<\/li>\r\n \t<li>[latex]-\\frac{2}{x}[\/latex]<\/li>\r\n \t<li>[latex]\\frac{2}{a}[\/latex]<\/li>\r\n \t<li>[latex]\\frac{2}{a+h}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\sqrt{5}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{11}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{23}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{-6x+5}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{6a+5}[\/latex]<\/li>\r\n \t<li>[latex]\\sqrt{6a+6h+5}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]9[\/latex]<\/li>\r\n \t<li>[latex]9[\/latex]<\/li>\r\n \t<li>[latex]9[\/latex]<\/li>\r\n \t<li>[latex]9[\/latex]<\/li>\r\n \t<li>[latex]9[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Domain: [latex]x\\ge \\frac{1}{8}[\/latex]; Range: [latex]y\\ge 0[\/latex]; Zeros: [latex]x=\\frac{1}{8}[\/latex]; no [latex]y[\/latex]-intercepts<\/li>\r\n \t<li>Domain: [latex]x\\ge -2[\/latex]; Range: [latex]y\\ge -1[\/latex]; Zeros: [latex]x=-1[\/latex]; [latex]y[\/latex]-intercepts: [latex]y=-1+\\sqrt{2}[\/latex]<\/li>\r\n \t<li>Domain: [latex]x\\ne 4[\/latex]; Range: [latex]y\\ne 0[\/latex]; no [latex]x[\/latex]-intercept; [latex]y[\/latex]-intercept: [latex]y=-\\frac{3}{4}[\/latex]<\/li>\r\n \t<li>Domain: [latex]x&gt;5[\/latex]; Range: [latex]y&gt;0[\/latex]; no intercepts<\/li>\r\n \t<li>\r\n<table id=\"fs-id1170572548974\" class=\"unnumbered\" summary=\"A table with 7 rows and 2 columns. The first column is labeled \u201cx\u201d and has the values \u201c-3; -2; -1; 0; 1; 2; 3\u201d. The second column is labeled \u201cy\u201d and the values are \u201c-15; -12; -9; -6; -3; 0; 3\u201d.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<td>[latex]\u221215[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22122[\/latex]<\/td>\r\n<td>[latex]\u221212[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22121[\/latex]<\/td>\r\n<td>[latex]\u22129[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]\u22126[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202143\/CNX_Calc_Figure_01_01_202.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -3 to 3. The graph is of the function \u201cf(x) = 3x - 6\u201d, which is an increasing straight line. The function has an x intercept at (2, 0) and the y intercept is not shown.\" \/><\/li>\r\n \t<li>\r\n<table id=\"fs-id1170572547867\" class=\"unnumbered\" summary=\"A table with 7 rows and 2 columns. The first column is labeled \u201cx\u201d and has the values \u201c-3; -2; -1; 0; 1; 2; 3\u201d. The second column is labeled \u201cy\u201d and the values are \u201c6; 4; 2; 0; 2; 4; 6\u201d.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22122[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22121[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]6[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202145\/CNX_Calc_Figure_01_01_204.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -2 to 6. The graph is of the function \u201cf(x) = 2 times the absolute value of x\u201d. The function decreases in a straight line until it hits the origin, then begins to increase in a straight line. The function x intercept and y intercept are at the origin.\" \/><\/li>\r\n \t<li>\r\n<table id=\"fs-id1170572545096\" class=\"unnumbered\" summary=\"A table with 7 rows and 2 columns. The first column is labeled \u201cx\u201d and has the values \u201c-3; -2; -1; 0; 1; 2; 3\u201d. The second column is labeled \u201cy\u201d and the values are \u201c-27; -8; -1; 0; 1; 8; 27\u201d.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<th>[latex]x[\/latex]<\/th>\r\n<th>[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22123[\/latex]<\/td>\r\n<td>[latex]\u221227[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22122[\/latex]<\/td>\r\n<td>[latex]\u22128[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\u22121[\/latex]<\/td>\r\n<td>[latex]\u22121[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>[latex]27[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0[\/latex]<\/td>\r\n<td>[latex]0[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202148\/CNX_Calc_Figure_01_01_206.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -27 to 27. The graph is of the function \u201cf(x) = x cubed\u201d. The curved function increases until it hits the origin, where it levels out and then becomes even. After the origin the graph begins to increase again. The x intercept and y intercept are both at the origin.\" \/><\/li>\r\n \t<li>Function\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain: all real numbers, Range: [latex]y\\ge 0[\/latex]<\/li>\r\n \t<li>[latex]x=\u00b11[\/latex]<\/li>\r\n \t<li>[latex]y=1[\/latex]<\/li>\r\n \t<li>[latex]-1 &lt; x&lt; 0[\/latex] and [latex]1 &lt; x &lt; \\infty [\/latex]<\/li>\r\n \t<li>[latex]\u2212\\infty &lt; x &lt; -1[\/latex] and [latex]0 &lt; x &lt; 1[\/latex]<\/li>\r\n \t<li>Not constant<\/li>\r\n \t<li>[latex]y[\/latex]-axis<\/li>\r\n \t<li>Even<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Function\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain: all real numbers, Range: [latex]-1.5\\le y\\le 1.5[\/latex]<\/li>\r\n \t<li>[latex]x=0[\/latex]<\/li>\r\n \t<li>[latex]y=0[\/latex]<\/li>\r\n \t<li>All real numbers<\/li>\r\n \t<li>None<\/li>\r\n \t<li>Not constant<\/li>\r\n \t<li>Origin<\/li>\r\n \t<li>Odd<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Function\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain: [latex]\u2212\\infty &gt; x &gt; \\infty [\/latex], Range: [latex]-2\\le y\\le 2[\/latex]<\/li>\r\n \t<li>[latex]x=0[\/latex]<\/li>\r\n \t<li>[latex]y=0[\/latex]<\/li>\r\n \t<li>[latex]-2 &gt; x &gt; 2[\/latex]<\/li>\r\n \t<li>Not decreasing<\/li>\r\n \t<li>[latex]\u2212\\infty &gt; x &gt; -2[\/latex] and [latex]2 &gt; x &gt; \\infty [\/latex]<\/li>\r\n \t<li>Origin<\/li>\r\n \t<li>Odd<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Function\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Domain: [latex]-4\\le x\\le 4[\/latex], Range: [latex]-4\\le y\\le 4[\/latex]<\/li>\r\n \t<li>[latex]x=1.2[\/latex]<\/li>\r\n \t<li>[latex]y=4[\/latex]<\/li>\r\n \t<li>Not increasing<\/li>\r\n \t<li>[latex]0 &gt; x &gt; 4[\/latex]<\/li>\r\n \t<li>[latex]-4 &gt; x &gt; 0[\/latex]<\/li>\r\n \t<li>No Symmetry<\/li>\r\n \t<li>Neither<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]5x^2+x-8[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]-5x^2+x-8[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]5x^3-40x^2[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]\\frac{x-8}{5x^2}; \\, x\\ne 0[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]-2x+6[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]-2x^2+2x+12[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]\u2212x^4+2x^3+12x^2-18x-27[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]-\\frac{x+3}{x+1}; \\, x\\ne \u22121,3[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]6+\\frac{2}{x}; \\, x\\ne 0[\/latex]<\/li>\r\n \t<li>6; [latex]x\\ne 0[\/latex]<\/li>\r\n \t<li>[latex]\\frac{6}{x}+\\frac{1}{x^2}; \\, x\\ne 0[\/latex]<\/li>\r\n \t<li>[latex]6x+1; \\, x\\ne 0[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]4x+3[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]4x+15[\/latex]; all real numbers<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]x^4-6x^2+16[\/latex]; all real numbers<\/li>\r\n \t<li>[latex]x^4+14x^2+46[\/latex]; all real numbers<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\frac{3x}{4+x}; \\, x\\ne 0,-4[\/latex]<\/li>\r\n \t<li>[latex]\\frac{4x+2}{3}; \\, x\\ne -\\frac{1}{2}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Yes, because there is only one winner for each year.<\/li>\r\n \t<li>No, because there are three teams that won more than once during the years 2001 to 2012.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]V(s)=s^3[\/latex]<\/li>\r\n \t<li>[latex]V(11.8)\\approx 1643[\/latex]; a cube of side length [latex]11.8[\/latex] each has a volume of approximately [latex]1643[\/latex] cubic units.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]N(x)=15x[\/latex]<\/li>\r\n \t<li>i. [latex]N(20)=15(20)=300[\/latex]; therefore, the vehicle can travel [latex]300[\/latex] mi on a full tank of gas. ii. [latex]N(15)=225[\/latex]; therefore, the vehicle can travel [latex]225[\/latex] mi on [latex]3\/4[\/latex] of a tank of gas.<\/li>\r\n \t<li>Domain: [latex]0\\le x\\le 20[\/latex]; Range: [latex][0,300][\/latex]<\/li>\r\n \t<li>The driver had to stop at least once, given that it takes approximately [latex]39[\/latex] gal of gas to drive a total of [latex]578[\/latex] mi.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]A(t)=A(r(t))=\\pi \u00b7(6-\\frac{5}{t^2+1})^2[\/latex]<\/li>\r\n \t<li>Exact: [latex]\\frac{121\\pi }{4}[\/latex]; approximately [latex]95[\/latex] cm<sup>2<\/sup><\/li>\r\n \t<li>[latex]C(t)=C(r(t))=2\\pi (6-\\frac{5}{t^2+1})[\/latex]<\/li>\r\n \t<li>Exact: [latex]11\\pi [\/latex]; approximately [latex]35[\/latex] cm<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202215\/CNX_Calc_Figure_01_01_215.jpg\" alt=\"An image of a graph. The y axis runs from 0 to 1800 and the x axis runs from 0 to 100. The graph is of the function \u201cS(x) = 8.5x + 750\u201d, which is a increasing straight line. The function has a y intercept at (0, 750) and the x intercept is not shown.\" \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]S(x)=8.5x+750[\/latex]<\/li>\r\n \t<li>[latex]$962.50[\/latex], [latex]$1090[\/latex], [latex]$1217.50[\/latex]<\/li>\r\n \t<li>[latex]77[\/latex] skateboards<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h2>Basic Classes of Functions<\/h2>\r\n<ol style=\"list-style-type: decimal;\">\r\n \t<li style=\"list-style-type: none;\">\r\n<ol style=\"list-style-type: decimal;\">\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\u22121[\/latex]<\/li>\r\n \t<li>Decreasing<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]3\/4[\/latex]<\/li>\r\n \t<li>Increasing<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]4\/3[\/latex]<\/li>\r\n \t<li>Increasing<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]0[\/latex]<\/li>\r\n \t<li>Horizontal<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>[latex]y=-6x+9[\/latex]<\/li>\r\n \t<li>[latex]y=\\frac{1}{3}x+4[\/latex]<\/li>\r\n \t<li>[latex]y=\\frac{1}{2}x[\/latex]<\/li>\r\n \t<li>[latex]y=\\frac{3}{5}x-3[\/latex]<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex](m=2, \\, b=-3)[\/latex]<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202334\/CNX_Calc_Figure_01_02_201.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows an increasing straight line function with a y intercept at (0, -3) and a x intercept at (1.5, 0).\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex](m=-6, \\, b=0)[\/latex]<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202340\/CNX_Calc_Figure_01_02_203.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a decreasing straight line function with a y intercept and x intercept both at the origin. There is an unlabeled point on the function at (0.5, -3).\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex](m=0, \\, b=-6)[\/latex]<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202344\/CNX_Calc_Figure_01_02_205.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -7 to 1. The graph shows a horizontal straight line function with a y intercept at (0, -6) and no x intercept.\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex](m=-\\frac{2}{3}, \\, b=2)[\/latex]<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202348\/CNX_Calc_Figure_01_02_207.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -4 to 4. The graph shows a decreasing straight line function with a y intercept at (0, 2) and a x intercept at (3, 0).\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]2[\/latex]<\/li>\r\n \t<li>[latex]\\frac{5}{2}, \\, -1[\/latex]<\/li>\r\n \t<li>[latex]\u22125[\/latex]<\/li>\r\n \t<li>Both ends rise<\/li>\r\n \t<li>Neither<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]2[\/latex]<\/li>\r\n \t<li>[latex]\\pm \\sqrt{2}[\/latex]<\/li>\r\n \t<li>[latex]\u22121[\/latex]<\/li>\r\n \t<li>Both ends rise<\/li>\r\n \t<li>Even<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]3[\/latex]<\/li>\r\n \t<li>[latex]0[\/latex], [latex]\\pm \\sqrt{3}[\/latex]<\/li>\r\n \t<li>[latex]0[\/latex]<\/li>\r\n \t<li>Left end rises, right end falls<\/li>\r\n \t<li>Odd<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202354\/CNX_Calc_Figure_01_02_210.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a parabolic function that decreases until the point (-3, 1), then begins increasing. The y intercept is not shown and there are no x intercepts. There are two unplotted points at (-4, 2) and (-2, 2).\" \/><\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202358\/CNX_Calc_Figure_01_02_212.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 20 and the y axis runs from -8 to 2. The graph shows a curved function that begins at the point (0, -1), then begins decreasing. The y intercept is at (0, -1) and there is no x intercept. There is an unplotted point at (9, -4).\" \/><\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202408\/CNX_Calc_Figure_01_02_215.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a function that starts at point (-2, 2), where it begins to increase until the point (0, 4). After the point (0, 4), the function becomes a horizontal line and stays that way until the point (2, 4). After the point (2, 4), the function begins to decrease until the point (4, 2), where the function ends.\" \/><\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]13, \\, -3, \\, 5[\/latex]<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202412\/CNX_Calc_Figure_01_02_217.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a function that has two pieces. The first piece is a decreasing curve that ends at the point (0, -3). The second piece is an increasing line that begins at the point (0, -3). The function has a x intercepts at the approximate point (1.7, 0) and the point (0.75, 0) and a y intercept at (0, -3).\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\frac{-3}{2}, \\, \\frac{-1}{2}, \\, 4[\/latex]<\/li>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202417\/CNX_Calc_Figure_01_02_219.jpg\" alt=\"An image of a graph. The x axis runs from -10 to 10 and the y axis runs from -10 to 10. The graph is of a function that begins slightly below the x axis and begins to decrease. As the function approaches the unplotted vertical line of \u201cx = 2\u201d, it decreases at a faster rate but never reaches the line \u201cx = 2\u201d. On the right side of the unplotted line \u201cx = 2\u201d, the function starts at the top of graph and begins decreasing and approaches the unplotted horizontal line \u201cy = 0\u201d, but never reaches \u201cy = 0\u201d. There function also includes a plotted point at (2, 4). There is a y intercept at (0, -1.5) and no x intercept.\" \/><\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>True, because [latex]n=3[\/latex]<\/li>\r\n \t<li>False, because [latex]f(x)=x^b[\/latex] - where [latex]b[\/latex] is a real-valued constant - is a power function.\u00a0 Exponential functions are of the form [latex]f(x)=b^x[\/latex], where [latex]b[\/latex] is a real-valued constant.<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]V(t)=-2733t+20500[\/latex]<\/li>\r\n \t<li>[latex](0, 20500)[\/latex] means that the initial purchase price of the equipment is [latex]$20,500[\/latex]; [latex](7.5,0)[\/latex] means that in [latex]7.5[\/latex] years the computer equipment has no value.<\/li>\r\n \t<li>[latex]$6835[\/latex]<\/li>\r\n \t<li>In approximately [latex]6.4[\/latex] years<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]C=0.75x+125[\/latex]<\/li>\r\n \t<li>[\/latex]$245[latex]<\/li>\r\n \t<li>[latex]167[\/latex] cupcakes<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]V(t)=-1500t+26,000[\/latex]<\/li>\r\n \t<li>In [latex]4[\/latex] years, the value of the car is [latex]$20,000[\/latex].<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>[latex]$30,337.50[\/latex]<\/li>\r\n \t<li>[latex]96\\%[\/latex] of the total capacity<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<h2 class=\"entry-title\">Review of Functions<\/h2>\n<ol style=\"list-style-type: decimal;\">\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain = [latex]\\{-3,-2,-1,0,1,2,3\\}[\/latex], range = [latex]\\{0,1,4,9\\}[\/latex]<\/li>\n<li>Yes, a function<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain = [latex]\\{0,1,2,3\\}[\/latex], range = [latex]\\{-3,-2,-1,0,1,2,3\\}[\/latex]<\/li>\n<li>No, not a function<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain = [latex]\\{3,5,8,10,15,21,33\\}[\/latex], range = [latex]\\{0,1,2,3\\}[\/latex]<\/li>\n<li>Yes, a function<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]-2[\/latex]<\/li>\n<li>[latex]3[\/latex]<\/li>\n<li>[latex]13[\/latex]<\/li>\n<li>[latex]-5x-2[\/latex]<\/li>\n<li>[latex]5a-2[\/latex]<\/li>\n<li>[latex]5a+5h-2[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Undefined<\/li>\n<li>[latex]2[\/latex]<\/li>\n<li>[latex]\\frac{2}{3}[\/latex]<\/li>\n<li>[latex]-\\frac{2}{x}[\/latex]<\/li>\n<li>[latex]\\frac{2}{a}[\/latex]<\/li>\n<li>[latex]\\frac{2}{a+h}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\sqrt{5}[\/latex]<\/li>\n<li>[latex]\\sqrt{11}[\/latex]<\/li>\n<li>[latex]\\sqrt{23}[\/latex]<\/li>\n<li>[latex]\\sqrt{-6x+5}[\/latex]<\/li>\n<li>[latex]\\sqrt{6a+5}[\/latex]<\/li>\n<li>[latex]\\sqrt{6a+6h+5}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]9[\/latex]<\/li>\n<li>[latex]9[\/latex]<\/li>\n<li>[latex]9[\/latex]<\/li>\n<li>[latex]9[\/latex]<\/li>\n<li>[latex]9[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Domain: [latex]x\\ge \\frac{1}{8}[\/latex]; Range: [latex]y\\ge 0[\/latex]; Zeros: [latex]x=\\frac{1}{8}[\/latex]; no [latex]y[\/latex]-intercepts<\/li>\n<li>Domain: [latex]x\\ge -2[\/latex]; Range: [latex]y\\ge -1[\/latex]; Zeros: [latex]x=-1[\/latex]; [latex]y[\/latex]-intercepts: [latex]y=-1+\\sqrt{2}[\/latex]<\/li>\n<li>Domain: [latex]x\\ne 4[\/latex]; Range: [latex]y\\ne 0[\/latex]; no [latex]x[\/latex]-intercept; [latex]y[\/latex]-intercept: [latex]y=-\\frac{3}{4}[\/latex]<\/li>\n<li>Domain: [latex]x>5[\/latex]; Range: [latex]y>0[\/latex]; no intercepts<\/li>\n<li>\n<table id=\"fs-id1170572548974\" class=\"unnumbered\" summary=\"A table with 7 rows and 2 columns. The first column is labeled \u201cx\u201d and has the values \u201c-3; -2; -1; 0; 1; 2; 3\u201d. The second column is labeled \u201cy\u201d and the values are \u201c-15; -12; -9; -6; -3; 0; 3\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\u22123[\/latex]<\/td>\n<td>[latex]\u221215[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]\u22123[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\u22122[\/latex]<\/td>\n<td>[latex]\u221212[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\u22121[\/latex]<\/td>\n<td>[latex]\u22129[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]\u22126[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202143\/CNX_Calc_Figure_01_01_202.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -3 to 3. The graph is of the function \u201cf(x) = 3x - 6\u201d, which is an increasing straight line. The function has an x intercept at (2, 0) and the y intercept is not shown.\" \/><\/li>\n<li>\n<table id=\"fs-id1170572547867\" class=\"unnumbered\" summary=\"A table with 7 rows and 2 columns. The first column is labeled \u201cx\u201d and has the values \u201c-3; -2; -1; 0; 1; 2; 3\u201d. The second column is labeled \u201cy\u201d and the values are \u201c6; 4; 2; 0; 2; 4; 6\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\u22123[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\u22122[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\u22121[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]6[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202145\/CNX_Calc_Figure_01_01_204.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -2 to 6. The graph is of the function \u201cf(x) = 2 times the absolute value of x\u201d. The function decreases in a straight line until it hits the origin, then begins to increase in a straight line. The function x intercept and y intercept are at the origin.\" \/><\/li>\n<li>\n<table id=\"fs-id1170572545096\" class=\"unnumbered\" summary=\"A table with 7 rows and 2 columns. The first column is labeled \u201cx\u201d and has the values \u201c-3; -2; -1; 0; 1; 2; 3\u201d. The second column is labeled \u201cy\u201d and the values are \u201c-27; -8; -1; 0; 1; 8; 27\u201d.\">\n<thead>\n<tr valign=\"top\">\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<th>[latex]x[\/latex]<\/th>\n<th>[latex]y[\/latex]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\u22123[\/latex]<\/td>\n<td>[latex]\u221227[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\u22122[\/latex]<\/td>\n<td>[latex]\u22128[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>[latex]8[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\u22121[\/latex]<\/td>\n<td>[latex]\u22121[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>[latex]27[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0[\/latex]<\/td>\n<td>[latex]0[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202148\/CNX_Calc_Figure_01_01_206.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -27 to 27. The graph is of the function \u201cf(x) = x cubed\u201d. The curved function increases until it hits the origin, where it levels out and then becomes even. After the origin the graph begins to increase again. The x intercept and y intercept are both at the origin.\" \/><\/li>\n<li>Function\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain: all real numbers, Range: [latex]y\\ge 0[\/latex]<\/li>\n<li>[latex]x=\u00b11[\/latex]<\/li>\n<li>[latex]y=1[\/latex]<\/li>\n<li>[latex]-1 < x< 0[\/latex] and [latex]1 < x < \\infty[\/latex]<\/li>\n<li>[latex]\u2212\\infty < x < -1[\/latex] and [latex]0 < x < 1[\/latex]<\/li>\n<li>Not constant<\/li>\n<li>[latex]y[\/latex]-axis<\/li>\n<li>Even<\/li>\n<\/ol>\n<\/li>\n<li>Function\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain: all real numbers, Range: [latex]-1.5\\le y\\le 1.5[\/latex]<\/li>\n<li>[latex]x=0[\/latex]<\/li>\n<li>[latex]y=0[\/latex]<\/li>\n<li>All real numbers<\/li>\n<li>None<\/li>\n<li>Not constant<\/li>\n<li>Origin<\/li>\n<li>Odd<\/li>\n<\/ol>\n<\/li>\n<li>Function\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain: [latex]\u2212\\infty > x > \\infty[\/latex], Range: [latex]-2\\le y\\le 2[\/latex]<\/li>\n<li>[latex]x=0[\/latex]<\/li>\n<li>[latex]y=0[\/latex]<\/li>\n<li>[latex]-2 > x > 2[\/latex]<\/li>\n<li>Not decreasing<\/li>\n<li>[latex]\u2212\\infty > x > -2[\/latex] and [latex]2 > x > \\infty[\/latex]<\/li>\n<li>Origin<\/li>\n<li>Odd<\/li>\n<\/ol>\n<\/li>\n<li>Function\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Domain: [latex]-4\\le x\\le 4[\/latex], Range: [latex]-4\\le y\\le 4[\/latex]<\/li>\n<li>[latex]x=1.2[\/latex]<\/li>\n<li>[latex]y=4[\/latex]<\/li>\n<li>Not increasing<\/li>\n<li>[latex]0 > x > 4[\/latex]<\/li>\n<li>[latex]-4 > x > 0[\/latex]<\/li>\n<li>No Symmetry<\/li>\n<li>Neither<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]5x^2+x-8[\/latex]; all real numbers<\/li>\n<li>[latex]-5x^2+x-8[\/latex]; all real numbers<\/li>\n<li>[latex]5x^3-40x^2[\/latex]; all real numbers<\/li>\n<li>[latex]\\frac{x-8}{5x^2}; \\, x\\ne 0[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]-2x+6[\/latex]; all real numbers<\/li>\n<li>[latex]-2x^2+2x+12[\/latex]; all real numbers<\/li>\n<li>[latex]\u2212x^4+2x^3+12x^2-18x-27[\/latex]; all real numbers<\/li>\n<li>[latex]-\\frac{x+3}{x+1}; \\, x\\ne \u22121,3[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]6+\\frac{2}{x}; \\, x\\ne 0[\/latex]<\/li>\n<li>6; [latex]x\\ne 0[\/latex]<\/li>\n<li>[latex]\\frac{6}{x}+\\frac{1}{x^2}; \\, x\\ne 0[\/latex]<\/li>\n<li>[latex]6x+1; \\, x\\ne 0[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]4x+3[\/latex]; all real numbers<\/li>\n<li>[latex]4x+15[\/latex]; all real numbers<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]x^4-6x^2+16[\/latex]; all real numbers<\/li>\n<li>[latex]x^4+14x^2+46[\/latex]; all real numbers<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\frac{3x}{4+x}; \\, x\\ne 0,-4[\/latex]<\/li>\n<li>[latex]\\frac{4x+2}{3}; \\, x\\ne -\\frac{1}{2}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Yes, because there is only one winner for each year.<\/li>\n<li>No, because there are three teams that won more than once during the years 2001 to 2012.<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]V(s)=s^3[\/latex]<\/li>\n<li>[latex]V(11.8)\\approx 1643[\/latex]; a cube of side length [latex]11.8[\/latex] each has a volume of approximately [latex]1643[\/latex] cubic units.<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]N(x)=15x[\/latex]<\/li>\n<li>i. [latex]N(20)=15(20)=300[\/latex]; therefore, the vehicle can travel [latex]300[\/latex] mi on a full tank of gas. ii. [latex]N(15)=225[\/latex]; therefore, the vehicle can travel [latex]225[\/latex] mi on [latex]3\/4[\/latex] of a tank of gas.<\/li>\n<li>Domain: [latex]0\\le x\\le 20[\/latex]; Range: [latex][0,300][\/latex]<\/li>\n<li>The driver had to stop at least once, given that it takes approximately [latex]39[\/latex] gal of gas to drive a total of [latex]578[\/latex] mi.<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]A(t)=A(r(t))=\\pi \u00b7(6-\\frac{5}{t^2+1})^2[\/latex]<\/li>\n<li>Exact: [latex]\\frac{121\\pi }{4}[\/latex]; approximately [latex]95[\/latex] cm<sup>2<\/sup><\/li>\n<li>[latex]C(t)=C(r(t))=2\\pi (6-\\frac{5}{t^2+1})[\/latex]<\/li>\n<li>Exact: [latex]11\\pi[\/latex]; approximately [latex]35[\/latex] cm<\/li>\n<\/ol>\n<\/li>\n<li><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202215\/CNX_Calc_Figure_01_01_215.jpg\" alt=\"An image of a graph. The y axis runs from 0 to 1800 and the x axis runs from 0 to 100. The graph is of the function \u201cS(x) = 8.5x + 750\u201d, which is a increasing straight line. The function has a y intercept at (0, 750) and the x intercept is not shown.\" \/>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]S(x)=8.5x+750[\/latex]<\/li>\n<li>[latex]$962.50[\/latex], [latex]$1090[\/latex], [latex]$1217.50[\/latex]<\/li>\n<li>[latex]77[\/latex] skateboards<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h2>Basic Classes of Functions<\/h2>\n<ol style=\"list-style-type: decimal;\">\n<li style=\"list-style-type: none;\">\n<ol style=\"list-style-type: decimal;\">\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\u22121[\/latex]<\/li>\n<li>Decreasing<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]3\/4[\/latex]<\/li>\n<li>Increasing<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]4\/3[\/latex]<\/li>\n<li>Increasing<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]0[\/latex]<\/li>\n<li>Horizontal<\/li>\n<\/ol>\n<\/li>\n<li>[latex]y=-6x+9[\/latex]<\/li>\n<li>[latex]y=\\frac{1}{3}x+4[\/latex]<\/li>\n<li>[latex]y=\\frac{1}{2}x[\/latex]<\/li>\n<li>[latex]y=\\frac{3}{5}x-3[\/latex]<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex](m=2, \\, b=-3)[\/latex]<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202334\/CNX_Calc_Figure_01_02_201.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows an increasing straight line function with a y intercept at (0, -3) and a x intercept at (1.5, 0).\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex](m=-6, \\, b=0)[\/latex]<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202340\/CNX_Calc_Figure_01_02_203.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a decreasing straight line function with a y intercept and x intercept both at the origin. There is an unlabeled point on the function at (0.5, -3).\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex](m=0, \\, b=-6)[\/latex]<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202344\/CNX_Calc_Figure_01_02_205.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -7 to 1. The graph shows a horizontal straight line function with a y intercept at (0, -6) and no x intercept.\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex](m=-\\frac{2}{3}, \\, b=2)[\/latex]<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202348\/CNX_Calc_Figure_01_02_207.jpg\" alt=\"An image of a graph. The x axis runs from -3 to 3 and the y axis runs from -4 to 4. The graph shows a decreasing straight line function with a y intercept at (0, 2) and a x intercept at (3, 0).\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]2[\/latex]<\/li>\n<li>[latex]\\frac{5}{2}, \\, -1[\/latex]<\/li>\n<li>[latex]\u22125[\/latex]<\/li>\n<li>Both ends rise<\/li>\n<li>Neither<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]2[\/latex]<\/li>\n<li>[latex]\\pm \\sqrt{2}[\/latex]<\/li>\n<li>[latex]\u22121[\/latex]<\/li>\n<li>Both ends rise<\/li>\n<li>Even<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]3[\/latex]<\/li>\n<li>[latex]0[\/latex], [latex]\\pm \\sqrt{3}[\/latex]<\/li>\n<li>[latex]0[\/latex]<\/li>\n<li>Left end rises, right end falls<\/li>\n<li>Odd<\/li>\n<\/ol>\n<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202354\/CNX_Calc_Figure_01_02_210.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a parabolic function that decreases until the point (-3, 1), then begins increasing. The y intercept is not shown and there are no x intercepts. There are two unplotted points at (-4, 2) and (-2, 2).\" \/><\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202358\/CNX_Calc_Figure_01_02_212.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 20 and the y axis runs from -8 to 2. The graph shows a curved function that begins at the point (0, -1), then begins decreasing. The y intercept is at (0, -1) and there is no x intercept. There is an unplotted point at (9, -4).\" \/><\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202408\/CNX_Calc_Figure_01_02_215.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph shows a function that starts at point (-2, 2), where it begins to increase until the point (0, 4). After the point (0, 4), the function becomes a horizontal line and stays that way until the point (2, 4). After the point (2, 4), the function begins to decrease until the point (4, 2), where the function ends.\" \/><\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]13, \\, -3, \\, 5[\/latex]<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202412\/CNX_Calc_Figure_01_02_217.jpg\" alt=\"An image of a graph. The x axis runs from -5 to 5 and the y axis runs from -5 to 5. The graph is of a function that has two pieces. The first piece is a decreasing curve that ends at the point (0, -3). The second piece is an increasing line that begins at the point (0, -3). The function has a x intercepts at the approximate point (1.7, 0) and the point (0.75, 0) and a y intercept at (0, -3).\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\frac{-3}{2}, \\, \\frac{-1}{2}, \\, 4[\/latex]<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2332\/2018\/01\/11202417\/CNX_Calc_Figure_01_02_219.jpg\" alt=\"An image of a graph. The x axis runs from -10 to 10 and the y axis runs from -10 to 10. The graph is of a function that begins slightly below the x axis and begins to decrease. As the function approaches the unplotted vertical line of \u201cx = 2\u201d, it decreases at a faster rate but never reaches the line \u201cx = 2\u201d. On the right side of the unplotted line \u201cx = 2\u201d, the function starts at the top of graph and begins decreasing and approaches the unplotted horizontal line \u201cy = 0\u201d, but never reaches \u201cy = 0\u201d. There function also includes a plotted point at (2, 4). There is a y intercept at (0, -1.5) and no x intercept.\" \/><\/li>\n<\/ol>\n<\/li>\n<li>True, because [latex]n=3[\/latex]<\/li>\n<li>False, because [latex]f(x)=x^b[\/latex] &#8211; where [latex]b[\/latex] is a real-valued constant &#8211; is a power function.\u00a0 Exponential functions are of the form [latex]f(x)=b^x[\/latex], where [latex]b[\/latex] is a real-valued constant.<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]V(t)=-2733t+20500[\/latex]<\/li>\n<li>[latex](0, 20500)[\/latex] means that the initial purchase price of the equipment is [latex]$20,500[\/latex]; [latex](7.5,0)[\/latex] means that in [latex]7.5[\/latex] years the computer equipment has no value.<\/li>\n<li>[latex]$6835[\/latex]<\/li>\n<li>In approximately [latex]6.4[\/latex] years<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]C=0.75x+125[\/latex]<\/li>\n<li>[\/latex]$245[latex]<\/li>\n<li>[latex]167[\/latex] cupcakes<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]V(t)=-1500t+26,000[\/latex]<\/li>\n<li>In [latex]4[\/latex] years, the value of the car is [latex]$20,000[\/latex].<\/li>\n<\/ol>\n<\/li>\n<li>[latex]$30,337.50[\/latex]<\/li>\n<li>[latex]96\\%[\/latex] of the total capacity<\/li>\n<\/ol>\n<\/li>\n<\/ol>\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":108,"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\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/148"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/148\/revisions"}],"predecessor-version":[{"id":161,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/148\/revisions\/161"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/108"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/148\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=148"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=148"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=148"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}