Precalculus 2014
67

 PAGE: 33 SET: Exercises PROBLEM: 67

The function is .

Graph :

Graph the function :

Observe the graph:

The function is even, because the graph is symmetric with respect to the -axis.

Algebraic conformation :

The function is .

Since , the function is an even function.

Since , the function is not an odd function.

Description for symmetry :

The function is .

Rewrite the function as .

Test algebraically symmetric with respect to the - axis.

Substitute for in .

Because   is not equivalent to , the function is not symmetric with respect to the -axis.

Test algebraically symmetric with respect to the -axis.

Substitute for in .

Because  is equivalent to , the function is symmetric with respect to the -axis.

Test algebraically symmetric with respect to the origin.

Substitute for and for in .

Because  is not equivalent to , the function is not  symmetric with respect to the origin.

Graph of the function :

The function is an even function.

The function is symmetric with respect to the -axis.

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