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Chapter 2: Q 42. (page 90)

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.
h(x)=xx2-1

Short Answer

Expert verified

The given functionh(x)=xx2-1is odd.

Step by step solution

01

Step 1. Write the given information and use the definition of odd and even function.

The given function is: h(x)=xx2-1

A function fis even if, for every number xin its domain, the number -xis also in the domain and f(-x)=f(x).

A function fis odd if, for every number xin its domain, the number -xis also in the domain andf(-x)=-f(x).

02

Step 2. Determine if the function is even.

Replace xby -xin the given function,

h(-x)=-x(-x)2-1=-xx2-1=-xx2-1

Since h(-x)鈮�h(x), the function is not even.

03

Step 3. Determine if the function is odd.

Find the function -h(x),

-h(x)=-xx2-1

Since role="math" localid="1645807726141" h(-x)=-h(x),his an odd function.

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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

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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
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