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 each term.

Apply the product rule to .

Raise to the power of .

Multiply by .

Multiply .

Multiply by .

Multiply by .

Check if .

Since , the function is not even.

The function is not even

The function is not even

Find .

Multiply by .

Apply the distributive property.

Multiply by .

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)=5x^3-x