Chapter 1.4, Problem 49E

To determine

To write: A function $g$ which is a reflection in the $x-\mathrm{axis}$ of $f(x)=\left|x\right|-5$ .

Answer to Problem 49E

Reflection in the $x-\mathrm{axis}$ is $g(x)=-\left|x\right|+5$.

Explanation of Solution

Given information: The given transformation of $f(x)=\left|x\right|-5$ .

Calculation: We have to find the function $g$ which is a reflection in the $x-\mathrm{axis}$ of $f(x)=\left|x\right|-5$ .

A reflection in the $x-\mathrm{axis}$ changes the sign of each output value.

  $\begin{array}{l}g(x)=-f(x)\\ g(x)=-(\left|x\right|-5)\\ g(x)=-\left|x\right|+5\end{array}$

Therefore reflection in the $x-\mathrm{axis}$ is $g(x)=-\left|x\right|+5$ .