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Chapter 2: Q. 19 (page 124)

Determine(algebraically)whethere the given function is even, odd,or neither.

g(x)=4+x21+x4

Short Answer

Expert verified

The giveng(x)=4+x21+x4is an even function

Step by step solution

01

Step 1.Given information

The given functiong(x)=4+x21+x4

02

Step 2.Determine the given function is even,odd or neither.

The function is even if g(-x)=g(x)and odd if g(-x)=-g(x).If none of these conditions are satisfied.

Find g(-x) by replacing -x for x in the given function.

role="math" localid="1645958483910" g(-x)=4+(-x)21+(-x)4=4+x21+x2=g(x)

Sinceg(-x)=g(x).We can conclude that the functiong(x)is even.

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Most popular questions from this chapter

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 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

Exploration Graph y=x2,y=x4, and y=x6 on the same screen. What do you notice is the same about each graph? What do you notice that is different?

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

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