Chapter 2: Q. 34 (page 113)

If $(4, 2)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = f 2 (x)$ ?

Short Answer

Expert verified

The point $(2, 2)$ lies on the graph of $y = f (2 x)$ so the option cis correct

Step by step solution

Step 1. Given data

The point $(4, 2)$ lies on the graph of the function $y = f (x)$

transformed function is $y = f (2 x)$

Step 2. Explanation of correct option C

Point $(4, 2)$ lies on $y = f (x)$

so $f (4) = 2$

$y = f (x)$ stretched horizontally for $y = f (2 x)$

so y coordinate of $y = f (2 x)$ at $x = 2$

$y = f (2 x) y = f (2 \times 2) y = f (4) y = 2$

point $(2, 2)$ lies on $y = f (2 x)$ so option bis correct.

Step 3. explanation of incorrect options

xcoordinate of $y = f (2 x)$ is half of xcoordinate of $y = f (x)$ so $(4, 1)$ cannot lie on $y = f (2 x)$
xcoordinate of $y = f (2 x)$ is half of xcoordinate of $y = f (x)$ so $(8, 2)$ cannot lie on $y = f (2 x)$
xcoordinate of $y = f (2 x)$ is half of xcoordinate of $y = f (x)$ so $(4, 4)$ cannot lie on $y = f (2 x)$

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If $(4, 2)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = f 2 (x)$ ?

Short Answer

Step by step solution

Step 1. Given data

Step 2. Explanation of correct option C

Step 3. explanation of incorrect options

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If 4,2is a point on the graph of y=f(x), which of the following points must be on the graph of y=f2(x)?

Short Answer

Step by step solution

Step 1. Given data

Step 2. Explanation of correct option C

Step 3. explanation of incorrect options

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

If $(4, 2)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = f 2 (x)$ ?