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Chapter 2: Q.40 (page 90)

Determine algebraically whether each function is even, odd, or neither.

fx=2x2+13

Short Answer

Expert verified

fxis an even function.

Step by step solution

01

Given information.

The function, fx=2x2+13.

02

Write definition of even function and odd function.

  • A function fxis said to be an even function if f-x=fx.
  • A functionfxis said to be an odd function iff-x=-fx.
03

Calculate f-x.

Replace xby -xinto the function fx=2x2+13.

width="147">f-x=2-x2+13=2x2+13=fx

Clearly, f-x=fx

So by definition,fxis an even function.

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Most popular questions from this chapter

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

g(x)=x2+3x2-1

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.

f(x)=x-13+2

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

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.

f(x)=-x

True or False

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

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