Rates of Change and Behavior of Graphs: Learn It 3

Behaviors of Functions Cont.

We will now return to our toolkit functions and discuss their graphical behavior in the table below.

Function	Increasing/Decreasing	Example
Constant Function[latex]f\left(x\right)={c}[/latex]	Neither increasing nor decreasing	Constant function
Identity Function[latex]f\left(x\right)={x}[/latex]	Increasing	Identity Function
Quadratic Function[latex]f\left(x\right)={x}^{2}[/latex]	Increasing on [latex]\left(0,\infty\right)[/latex]Decreasing on [latex]\left(-\infty,0\right)[/latex] Minimum at [latex]x=0[/latex]	Quadratic function
Cubic Function[latex]f\left(x\right)={x}^{3}[/latex]	Increasing	Cubic function
Reciprocal[latex]f\left(x\right)=\frac{1}{x}[/latex]	Decreasing [latex]\left(-\infty,0\right)\cup\left(0,\infty\right)[/latex]	Reciprocal function
Reciprocal Squared[latex]f\left(x\right)=\frac{1}{{x}^{2}}[/latex]	Increasing on [latex]\left(-\infty,0\right)[/latex]Decreasing on [latex]\left(0,\infty\right)[/latex]	Reciprocal squared function
Cube Root[latex]f\left(x\right)=\sqrt[3]{x}[/latex]	Increasing	Cube root function
Square Root[latex]f\left(x\right)=\sqrt{x}[/latex]	Increasing on [latex]\left(0,\infty\right)[/latex]	Square root function
Absolute Value[latex]f\left(x\right)=\|x\|[/latex]	Increasing on [latex]\left(0,\infty\right)[/latex]Decreasing on [latex]\left(-\infty,0\right)[/latex] Minimum at [latex]x=0[/latex]	Absolute value function