Chapter 1.6, Problem 31E

Solution

$\left(a\right)$

Find the equation of the reflection of $f$ across the x-axis.

  $f\left(x\right)=\sqrt[3]{8x}$

Given:

  $f\left(x\right)=\sqrt[3]{8x}$

Calculation:

For the reflection of $f\left(x\right)$ in the x-axis, use the following:

  $y=-f\left(x\right)=-\sqrt[3]{8x}$

Graph:

  

$\left(b\right)$

Find the equation of the reflection of $f$ across the y-axis.

  $f\left(x\right)=\sqrt[3]{8x}$

Given:

  $f\left(x\right)=\sqrt[3]{8x}$

Calculation:

For the reflection of $f\left(x\right)$ in the y-axis, use the following:

  $y=f\left(-x\right)=-\sqrt[3]{8\left(-x\right)}$

Graph: