Chapter 3.8, Problem 25PPS

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 $g(x)=\left|\frac{1}{4}x\right|$

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 $g(x)=\left|\frac{1}{4}x\right|=\{\begin{array}{l}-\frac{1}{4}x;x<0\\ \frac{1}{4}x;x\ge 0\end{array}$

Make a table of values for $g(x)=\left|\frac{1}{4}x\right|$

$x$	$-8$	$-1$	$0$	$4$	$8$
$g(x)$	$2$	$3$	$0$	$1$	$2$

The graph of $g(x)=\left|\frac{1}{4}x\right|$ is shown below.

  

Hence,

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

The transformation of $g(x)=\left|\frac{1}{4}x\right|$ is the horizontal stretch by the factor $1/4$ of $f(x)=\left|x\right|$ .