Chapter 3, Problem 75SGR

To determine

To describe: the transformation of the given function related to $f(x)=\left|x\right|$ .

Explanation of Solution

Given information:

The function $g(x)=-\left|x\right|$

Calculation:

The given function is a absolute value function.

That can be written as $g(x)=-\left|x\right|=\{\begin{array}{l}x;x<0\\ -x;x\ge 0\end{array}$

Make a table of values for $g(x)=-\left|x\right|$

$x$	$-5$	$-2$	$0$	$2$	$5$
$f(x)$	$-5$	$-2$	$0$	$-2$	$-5$

The graph of $g(x)=-\left|x\right|$ is shown below.

Hence,

The transformation of $g(x)=-\left|x\right|$ is the reflection across x- axis of the $f(x)=\left|x\right|$ .