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Q. 13

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Found in: Page 112

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 7–18, match each graph to one of the following functions:$\mathbit{A}\mathbf{.}y={x}^{2}+2\mathbit{B}\mathbf{.}y=-{x}^{2}+2\mathbit{C}.y=\left|x\right|+2\phantom{\rule{0ex}{0ex}}\mathbit{D}\mathbf{.}y=-\left|x\right|+2\mathbit{E}\mathbf{.}y={\left(x-2\right)}^{2}\mathbit{F}\mathbf{.}y=-{\left(x+2\right)}^{2}\phantom{\rule{0ex}{0ex}}\mathbit{G}\mathbf{.}y=\left|x-2\right|\mathbit{H}\mathbf{.}y=-\left|x+2\right|\mathbit{I}\mathbf{.}y=2{x}^{2}\phantom{\rule{0ex}{0ex}}\mathbit{J}\mathbf{.}y=-2{x}^{2}\mathbit{K}\mathbf{.}y=2\left|x\right|\mathbit{L}\mathbf{.}y=-2\left|x\right|$

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

See the 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

When the right side of the function $y=f\left(x\right)$ is multiplied by $-1$ the graph of the new function $y=-f\left(x\right)$ is the reflection about the x-axis of the graph of the function $y=f\left(x\right)$.

Thus, the function whose graph is the reflection of the graph of $y=\left|x\right|$ in the x-axis is $y=-\left|x\right|.$

The given graph is a reflection in the x-axis of the graph of the function $y=\left|x\right|$ but it is vertically stretched by a factor of $2.$

## Step 3. Stating the function of the graph

When the right side of a function $y=f\left(x\right)$ is multiplied by a positive number a, the graph of the new function $y=af\left(x\right)$ is obtained by multiplying each y-coordinate on the graph of $y=f\left(x\right)$ by a. The new graph is a vertically stretched $\left(ifa>1\right)$ version of the graph of $y=f\left(x\right).$

Since the graph is vertically stretched by factor of $2.$

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