Chapter 3.8, Problem 20PPS

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 $g(x)=2\left|x\right|$

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 $g(x)=2\left|x\right|=\{\begin{array}{l}-2x;x<0\\ 2x;x\ge 0\end{array}$

Make a table of values for $g(x)=2\left|x\right|$

$x$	$5$	$-1$	$0$	$1$	$5$
$g(x)$	$10$	$2$	$0$	$2$	$10$

The graph of $g(x)=2\left|x\right|$ is shown below.

  

Hence,

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

The transformation of $g(x)=2\left|x\right|$ is vertical stretch by the factor $2$ of $f(x)=\left|x\right|$ .