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Chapter 2: Q. 34 (page 113)

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

Expert verified

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

Step by step solution

01

Step 1. Given data

The point4,2lies on the graph of the functiony=f(x)

transformed function isy=f(2x)

02

Step 2. Explanation of correct option C 

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

so f(4)=2

y=f(x)stretched horizontally fory=f(2x)

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

y=f(2x)y=f(2脳2)y=f(4)y=2

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

03

Step 3. explanation of incorrect options 

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

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