Chapter 3, Problem 73SGR

To determine

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

Explanation of Solution

Given information:

The function $g(x)=\left|x\right|-4$

Calculation:

The given function is a absolute value function.

That can be written as $g(x)=\left|x\right|-4=\{\begin{array}{l}-x-4;x<4\\ \text{x-4 };x\ge 4\end{array}$

Make a table of values for $g(x)=\left|x\right|-4$

$x$	$-5$	$-2$	$0$	$2$	$5$
$f(x)$	$3$	$0$	$2$	$4$	$7$

The graph of $g(x)=\left|x\right|-4$ is shown below.

Hence,

The transformation of $g(x)=\left|x\right|-4$ is the $4$ units down shift of $f(x)=\left|x\right|$ by the factor $3.$