The function is .

Graph the function :

Observe the graph :

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

Algebraic conformation :

The function .

Since , the function is even.

Since , the function is not odd.

Description for symmetry :

The function .

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 even.

The function is symmetric with respect to the -axis.