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Expert-verified Found in: Page 103 ### Precalculus Enhanced with Graphing Utilities

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 $y=f\left(x\right)$.

See the step by step solution

## Step 1. Graph the first set of functions

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 $y={x}^{2}$.

## Step 2. Graph the second set of functions

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 $y=\left|x\right|$.

## Step 3. Conclusion

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 $y=f\left(x\right)$. ### Want to see more solutions like these? 