There are three types of symmetry:

1. X-Axis Symmetry

2. Y-Axis Symmetry

3. Origin Symmetry

If exists on the graph, then the graph is symmetric about the:

1. X-Axis if exists on the graph

2. Y-Axis if exists on the graph

3. Origin if exists on the graph

Check if the graph is symmetric about the x-axis by plugging in for .

Apply the product rule to .

Raise to the power of .

Multiply by .

Apply the product rule to .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Since the equation is identical to the original equation, it is symmetric to the x-axis.

Symmetric with respect to the x-axis

Check if the graph is symmetric about the y-axis by plugging in for .

Remove parentheses.

Since the equation is not identical to the original equation, it is not symmetric to the y-axis.

Not symmetric to the y-axis

Check if the graph is symmetric about the origin by plugging in for and for .

Remove parentheses.

Remove parentheses.

Simplify each term.

Apply the product rule to .

Raise to the power of .

Multiply by .

Apply the product rule to .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Multiply .

Multiply by .

Multiply by .

Simplify .

Simplify each term.

Apply the product rule to .

Raise to the power of .

Multiply by .

Apply the product rule to .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Raise to the power of .

Apply the distributive property.

Simplify.

Multiply .

Multiply by .

Multiply by .

Multiply by .

Since the equation is not identical to the original equation, it is not symmetric to the origin.

Not symmetric to the origin

Determine the symmetry.

Symmetric with respect to the x-axis

Find the Symmetry x=y^4-y^2+1