Chapter 10.2, Problem 27E

To determine

To find the transformation and compare the graph.

Answer to Problem 27E

Horizontal shift: right 4 units

Vertical shift: up 2 units

Stretch or shrink: none

Explanation of Solution

Given information: $f\left(x\right)=\sqrt[3]{x}$ and $g\left(x\right)=\sqrt[3]{x-4}+2$

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: right 4 units

Vertical shift: up 2 units

Stretch or shrink: none

 •  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 $g\left(x\right)=\sqrt[3]{x-4}+2$

  $\begin{array}{cccc}x& -4& 3& 4\\ g(x)& 0& 1& 2\end{array}$