Chapter 2: Q. 64 (page 103)

Exploration Graph $y = \sqrt{x}$ . Then on the same screen graph $y = \sqrt{- x}$ . What pattern do you observe? Now try $y = 2 x + 1$ and $y = 2 (- x) + 1$ . What do you conclude?

Short Answer

Expert verified

The graph of $y = \sqrt{- x}$ is the reflection about the $y$ -axis of the graph of $y = \sqrt{x}$ .

The same can be seen for the graph of $y = 2 x + 1$ and $y = 2 (- x) + 1$ .

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

Step by step solution

Step 1. Graph the first set of functions

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

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

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

Step 2. Graph the second set of functions

In the same coordinate plane draw the graphs of $y = 2 x + 1$ and $y = 2 (- x) + 1$ .

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

So it can be said that the graph of $y = 2 (- x) + 1$ is the reflection about the $y$ axis of the graph of $y = 2 x + 1$ .

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 $y$ axis of the graph of $y = f (x)$ .

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Exploration Graph $y = \sqrt{x}$ . Then on the same screen graph $y = \sqrt{- x}$ . What pattern do you observe? Now try $y = 2 x + 1$ and $y = 2 (- x) + 1$ . What do you conclude?

Short Answer

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. Then on the same screen graph y=-x. What pattern do you observe? Now try y=2x+1 and y=2(-x)+1. What do you conclude?

Short Answer

Step by step solution

Step 1. Graph the first set of functions

Step 2. Graph the second set of functions

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Logic and Functions

Probability and Statistics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Exploration Graph $y = \sqrt{x}$ . Then on the same screen graph $y = \sqrt{- x}$ . What pattern do you observe? Now try $y = 2 x + 1$ and $y = 2 (- x) + 1$ . What do you conclude?