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Chapter 2: Q. 31 (page 113)

If 3,6is a point on the graph of role="math" localid="1645806552504" y=f(x), which of the following points must be on the graph of y=f-(x)?

Short Answer

Expert verified

The point(3,-6)lies on the graph localid="1645811301127" y=-f(x) so the option cis correct.

Step by step solution

01

Step 1. Given data

The point(3,6)lies on the graph of the functiony=f(x).

transformed function isy=-f(x).

02

Step 2. Explanation of correct option C

Point(3,6)lies on y=f(x)

so f(3)=6

y=-f(x)is a reflection of y=f(x) about x-axis

so y coordinate of y=-f(x)atx=3

y=-f(3)y=-6

point (3,-6)lies on y=-f(x)so option C is correct.

03

Step 3. explanation of incorrect options

  • point(6,-3)does not lie ony=f(x)so(6,3)can not lie on y=-f(x)and option a is incorrect.
  • point6,3does not lie on y=f(x)so(6,-3)can not lie ony=-f(x)and option b is incorrect.
  • pointlocalid="1645808421822" (-3,-6)does not lie ony=f(x)so(-3,6)can not lie ony=-f(x)and option d is incorrect.

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