Determine if the function is odd, even, or neither in order to find the symmetry.

1. If odd, the function is symmetric about the origin.

2. If even, the function is symmetric about the y-axis.

Find by substituting for all occurrence of in .

Simplify the numerator.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify with factoring out.

Move the negative in front of the fraction.

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Factor out of .

Simplify the expression.

Rewrite as .

Multiply by .

Multiply by .

Check if .

Since , the function is not even.

The function is not even

The function is not even

Simplify the numerator.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Since , the function is odd.

The function is odd

The function is odd

Since the function is odd, it is symmetric about the origin.

Origin Symmetry

Since the function is not even, it is not symmetric about the y-axis.

No y-axis symmetry

Determine the symmetry of the function.

Origin symmetry

Find the Symmetry f(x)=(x^2-81)/x