College Algebra : Symmetry

Study concepts, example questions & explanations for College Algebra

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Example Questions

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Example Question #71 : Graphs

Consider the function .

Is  an even function, an odd function, or neither?

Possible Answers:

Even

Odd

Neither

Correct answer:

Even

Explanation:

A function  is even if, for each  in its domain,

.

It is odd if, for each  in its domain,

.

Substitute  for  in the definition:

Since  is an even function. 

Example Question #72 : Graphs

 is an even function. Let 

Is  an even function, an odd function, or neither?

Possible Answers:

Odd

Even

Neither

Correct answer:

Odd

Explanation:

A function  is even if, for each  in its domain,

.

It is odd if, for each  in its domain,

.

Substitute  for  in the definition of :

Since  is even, , so

This makes  an odd function. 

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