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Chapter 2: Q. 33 (page 113)

If (1,3)is a point on the graph of y=f(x), which of the following points must be on the graph ofy=2f(x)?

Short Answer

Expert verified

The point (1,6)lies on the graph ofy=2f(x)so the optionc is correct

Step by step solution

01

Step 1. Given data

The point 1,3lies on the graph of the functiony=f(x)

transformed function isy=2f(x)

02

Step 2. Explanation of correct option C 

Point (1,3)lies on y=f(x)

so f(1)=3

y=2f(x)is obtained by stretching y=f(x)vertically

so y coordinate ofy=2f(x)atx=1

y=2f(x)y=2f(1)y=2(3)y=6

point(1,6)lies ony=2f(x)so option cis correct.

03

Step 3. explanation of incorrect options 

  • y coordinate ofy=2f(x)is two times of y=f(x)so point1,32can not lie on it
  • y coordinate of y=2f(x)is two times ofy=f(x)so point (2,3)can not lie on it
  • y coordinate of y=2f(x) is two times of y=f(x)so point12,3can not lie on it

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Most popular questions from this chapter

True or False

The graph of y=-f(x)is the reflection about the x-axis of the graph of y=f(x).

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

h(x)=2x3

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.

h(x)=-x33x2-9

In Problems 19-26,write the function whose graph is the graph of y=x3but is:

Shifted to the right4 units
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