The function is .

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 even.

Since , the function is not odd.

Description for symmetry :

The function is .

Test algebraically symmetric with respect to the -axis.

Substitute for in .

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

Graph of the function :

.

The function is even.

The function is symmetric with respect to the -axis.