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Q. 18

Expert-verifiedFound in: Page 113

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

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

$\mathit{A}\mathbf{.}y={x}^{2}+2\mathit{B}\mathbf{.}y=-{x}^{2}+2\mathit{C}.y=\left|x\right|+2\phantom{\rule{0ex}{0ex}}\mathit{D}\mathbf{.}y=-\left|x\right|+2\mathit{E}\mathbf{.}y={(x-2)}^{2}\mathit{F}\mathbf{.}y=-{(x+2)}^{2}\phantom{\rule{0ex}{0ex}}\mathit{G}\mathbf{.}y=\left|x-2\right|\mathit{H}\mathbf{.}y=-\left|x+2\right|\mathit{I}\mathbf{.}y=2{x}^{2}\phantom{\rule{0ex}{0ex}}\mathit{J}\mathbf{.}y=-2{x}^{2}\mathit{K}\mathbf{.}y=2\left|x\right|\mathit{L}\mathbf{.}y=-2\left|x\right|$

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

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

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

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 $(ifa>1)$ version of the graph of $y=f\left(x\right).$

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

The function of the given graph is role="math" localid="1645865928495" $y=2\left|x\right|$ that matched to option K.

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