Chapter 3.8, Problem 22PPS

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 $g(x)=-3\left|x\right|$

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 $g(x)=-3\left|x\right|=\{\begin{array}{l}-3x;x<0\\ 3x;x\ge 0\end{array}$

Make a table of values for $g(x)=-3\left|x\right|$

$x$	$-10$	$-1$	$0$	$1$	$10$
$g(x)$	$-30$	$-3$	$0$	$-3$	$-30$

The graph of $g(x)=-3\left|x\right|$ is shown below.

  

Hence,

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

The transformation of $g(x)=-3\left|x\right|$ is the reflection over x-axis followed by vertical stretch by the factor $3$ of $f(x)=\left|x\right|$ .