Question

Graph each equation or inequality

$14. g\left(x\right)=\left|x+2\right|$

Short answer

The graph of the equation $g\left(x\right)=\left|x+2\right|$ is

Step-by-step solution

Step-1 – Apply the concept of absolute value function

The absolute value function, written as $f\left(x\right)=\left|x\right|$is defined as follows:

$f\left(x\right)=\left\{\begin{array}{c}-x\text{if}x<0\\ x\text{if}x\ge 0\end{array}\right.$

For examples, $\left|-2\right|=2;\left|2\right|=2;\left|3.5\right|=3.5;\left|-3.5\right|=3.5$

Step-2 – Make a Table of values 

Make a table of values such that the values satisfy the equation $g\left(x\right)=\left|x+2\right|$.

Choose a value of x and find the corresponding value of $g\left(x\right)$.

x	$x+2$	$\left|x+2\right|$
$-3$	-1	$1$
$-2$	0	0
$-1$	1	1
0	2	2
1	3	3

Step-3 – Graph the tabled values

By using the values in the table, graph the equation.