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Q. 63

Expert-verifiedFound in: Page 103

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

**Exploration** Graph $y={x}^{2}$. Then on the same screen graph $y=-{x}^{2}$. What pattern do you observe? Now try $y=\left|x\right|$ and $y=-\left|x\right|$. What do you conclude?

The graph of $y=-{x}^{2}$ is the reflection about the $x$-axis of the graph of role="math" localid="1645847739257" $y={x}^{2}$.

The same can be seen for the graph of $y=\left|x\right|$ and $y=-\left|x\right|$.

It can be concluded that the graph of $y=-f\left(x\right)$ is the reflection about the $x$ axis of the graph of $y=f\left(x\right)$.

In the same coordinate plane draw the graphs of $y={x}^{2}$ and $y=-{x}^{2}$.

It can be seen that both the graphs are reflections of each other about the $x$ axis.

So it can be said that the graph of $y=-{x}^{2}$ is the reflection about the $x$ axis of the graph of $y={x}^{2}$.

In the same coordinate plane draw the graphs of $y=\left|x\right|$ and $y=-\left|x\right|$.

Again, it can be seen that both the graphs are reflections of each other about the $x$ axis.

So it can be said that the graph of $y=-\left|x\right|$ is the reflection about the $x$ axis of the graph of $y=\left|x\right|$.

From the observation of the above two sets of functions, we can come to a conclusion that the graph of $y=-f\left(x\right)$ is the reflection about the $x$ axis of the graph of $y=f\left(x\right)$.

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