Chapter 10.2, Problem 24E

To determine

To compare the graph.

Answer to Problem 24E

Horizontal shift: none

Vertical shift: up 2 units

Stretch: Vertical Stretch

Explanation of Solution

Given information: $f\left(x\right)=\sqrt[3]{x}$ and $v\left(x\right)=\sqrt[3]{5x}+2$

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: up 2 units

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 $v\left(x\right)=\sqrt[3]{5x}+2$

  $\begin{array}{cccc}x& -2& -1& 0\\ v(x)& -0.2& 0.5& 2\end{array}$