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Q. 7

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:

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

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

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

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 $y={x}^{2}$ in the *x-*axis is $y=-{x}^{2}$.

The given graph is the reflection in the *x-*axis of the function $y={x}^{2}$ that is shifted vertically up by $2$ units.

So, the function of the given graph is role="math" localid="1645856662806" $y=-{x}^{2}+2$ that matched to option B.

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