Chapter 3.8, Problem 36PPS

a)

To determine

To make: a table of values for given function.

Explanation of Solution

Given information:

The function $f(x)=\left|2x\right|+3$

Consider the function $f(x)=\left|2x\right|+3=\{\begin{array}{l}-2x+3;x<0\\ (2x+3;x\ge 0\end{array}$

Make a table of values for $g(x)=|x-2|-5$

$x$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$
$g(x)$	$-13$	$11$	$9$	$7$	$5$	$3$	$5$	$7$	$9$	$11$	$13$

Hence,

The table of values are constructed for given function.

b)

To determine

To plot: the points on a coordinate grid of the given function.

Explanation of Solution

Given information:

The function $f(x)=\left|2x\right|+3$

The plot of the points of the function $f(x)=\left|2x\right|+3$ is shown below..

c)

To determine

To graph: the given function.

Explanation of Solution

Given information:

The function $f(x)=\left|2x\right|+3$

Graph the function $g(x)$.

.

d)

To determine

To explain: the difference between the graphs $f(x)=\left|2x\right|+3$ and $f(x)=|2x+3|$ .

Explanation of Solution

Given information:

The function $f(x)=\left|2x\right|+3$

Graph the functions $f(x)=\left|2x\right|+3\text{ and }f(x)=|2x+3|$.

Hence,

$f(x)=\left|2x\right|+3$ is the three units up shift of $f(x)=\left|2x\right|$ , where as

$f(x)=|2x+3|$ is the three units left shift of $f(x)=\left|2x\right|$ .