Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

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

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 $y = |x|$ and $y = - |x|$ .

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 $y = - |x|$ is the reflection about the $x$ axis of the graph of $y = |x|$ .

Step 3. Conclusion

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

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1. Graph the first set of functions

Step 2. Graph the second set of functions

Step 3. Conclusion

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Exploration Graph y=x2. Then on the same screen graph y=-x2. What pattern do you observe? Now try y=x and y=-x. What do you conclude?

Step by Step Solution

Step 1. Graph the first set of functions

Step 2. Graph the second set of functions

Step 3. Conclusion

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