Question

In Problems 7–18, match each graph to one of the following functions:

$$\begin{gathered} \mathit{A}\mathbf{.}y=x^2+2\mathit{B}\mathbf{.}y=-x^2+2\mathit{C}.y=\left|x\right|+2 \\ \mathit{D}\mathbf{.}y=-\left|x\right|+2\mathit{E}\mathbf{.}y={(x-2)}^2\mathit{F}\mathbf{.}y=-{(x+2)}^2 \\ \mathit{G}\mathbf{.}y=\left|x-2\right|\mathit{H}\mathbf{.}y=-\left|x+2\right|\mathit{I}\mathbf{.}y=2x^2 \\ \mathit{J}\mathbf{.}y=-2x^2\mathit{K}\mathbf{.}y=2\left|x\right|\mathit{L}\mathbf{.}y=-2\left|x\right| \end{gathered}$$

Short answer

The given graph is matched to the function$\mathit{G}\mathbf{.}\mathbf{}y=\left|x-2\right|.$

Step-by-step solution

Step 1. Given Information 

There is the given graph we have to match each graph to its functions.

Step 2. Identifying the function of the graph 

The given graph is similar of the function $y=\left|x\right|$but it is shifted horizontally to the right by $2$units.

If the argument x of a function f is replaced by $x-h,h>0,$the graph of the new function $y=f(x-h)$ is the graph of f shifted horizontally right hunits.

Since the graph of $y=\left|x\right|$is shifted horizontally right by $2$units.

The function of the given graph is$y=\left|x-2\right|$ that matched to the option G.