Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The given graph is matched to the function $\mathit{E}\mathbf{.}\mathbf{ }y={(x-2)}^2.$

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 to the graph of the function $y=x^2$ but is shifted horizontally 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 h units.

Thus, the graph of the function is $y={(x-2)}^2$ that matched to option E.