Chapter 10.2, Problem 23E

To determine

To compare the graph.

Answer to Problem 23E

Horizontal shift: none

Vertical shift: Down 1 unit

Stretch: Vertical Stretch

Explanation of Solution

Given information: $f\left(x\right)=\sqrt[3]{x}$ and $n\left(x\right)=\sqrt[3]{-8x}-1$

Formula Used: Ratio Property

Calculation:

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis.

Parent function: $f\left(x\right)=\sqrt[3]{x}$

Horizontal shift: none

Vertical shift: Down 1 unit

Stretch: Vertical Stretch

 •  Graph of $f\left(x\right)=\sqrt[3]{x}$

  $\begin{array}{cccc}x& 0& 1& 2\\ f(x)& 0& 1& 1.12\end{array}$

 •  Graph of $n\left(x\right)=\sqrt[3]{-8x}-1$

  $\begin{array}{cccc}x& -1& 0& 1\\ n(x)& 1& -1& -3\end{array}$