# Precalculus Examples

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 .

Find by substituting for all occurrence of in .

Reduce the expression by cancelling the common factors.

Rewrite as .

Multiply by to get .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

A function is even if .

Check if .

Since , the function is not even.

The function is not even

The function is not even

A function is odd if .

Simplify .

Multiply by to get .

Multiply by to get .

Since , the function is odd.

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