The function is $\"\"$ .

Graph the function $\"\"$ :

Observe the graph:

The function is odd, because the graph is symmetric with respect to the origin.

Algebraic conformation :

The function is $\"\"$ .

$\"\"$

Since $\"\"$ , the function is not even.

$\"\"$

Since $\"\"$ , the function is odd.

Description for symmetry :

The function is $\"\"$ .

Let $\"\"$ , $\"\"$ .

Rewrite the function as $\"\"$ .

Test algebraically symmetric with respect to the origin.

Substitute $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in $\"\"$ .

$\"\"$

Because $\"\"$ is equivalent to $\"\"$ , the function is symmetric with respect to the origin.

Graph of the function $\"\"$ :

The function $\"\"$ is odd.

The function is symmetric with respect to the origin.