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Q. 14

Expert-verifiedFound in: Page 112

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 $\mathit{C}\mathbf{.}\mathbf{}y=\left|x\right|+2.$

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

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

If a positive real number *k* is added to the outputs of a function $y=f\left(x\right),$ the graph of the new function $y=f\left(x\right)+k$ is the graph of *f *shifted vertically up *k *units.

Thus, the function of the graph is $y=\left|x\right|+2$ that matched to option C.

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