Chapter 3.8, Problem 1GP

To determine

To graph: the given function, to state the domain and range and then to describe the transformation of the given function related to $f(x)=\left|x\right|$ .

Explanation of Solution

Given information:

The function $g(x)=\left|x\right|-1$

Concept used:

Domain is the set of input values for which the function is defined.

Range is the set of output values for input values which are in domain.

Consider $g(x)=\left|x\right|-1=\{\begin{array}{l}-x-1;x<1\\ x-1x\ge 1\end{array}$

Make a table of values for $g(x)=\left|x\right|-1$

$x$	$-5$	$-1$	$0$	$1$	$5$
$g(x)$	$4$	$0$	$-1$	$0$	$4$

The graph of $g(x)=\left|x\right|-1$ is shown below.

  

Hence,

Domain is $(-\infty ,\infty )$ , Range is $[0,\infty )$

The transformation of $g(x)=\left|x\right|-1$ is the $1$ unit down shift of $f(x)=\left|x\right|$ .