Chapter 3.8, Problem 1CYU

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

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

$x$	$-4$	$-2$	$0$	$2$	$4$
$g(x)$	$5$	$3$	$1$	$3$	$5$

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

v

Hence,

Domain is $(-\infty ,\infty )$ , Range is $[1,\infty ).$

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