Behaviors of Functions Cont.
Analyzing the Toolkit Functions for Increasing or Decreasing Intervals
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 |  |
| Identity Function[latex]f\left(x\right)={x}[/latex] | Increasing |  |
| 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] |
 |
| Cubic Function[latex]f\left(x\right)={x}^{3}[/latex] | Increasing |  |
| Reciprocal[latex]f\left(x\right)=\frac{1}{x}[/latex] | Decreasing [latex]\left(-\infty,0\right)\cup\left(0,\infty\right)[/latex] |  |
| 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] |  |
| Cube Root[latex]f\left(x\right)=\sqrt[3]{x}[/latex] | Increasing |  |
| Square Root[latex]f\left(x\right)=\sqrt{x}[/latex] | Increasing on [latex]\left(0,\infty\right)[/latex] |  |
| 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] |
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