# Precalculus : Determine the Symmetry of an Equation

## Example Questions

### Example Question #1 : Determine The Symmetry Of An Equation

Is the following function symmetric across the y-axis? (Is it an even function?)

This isn't even a function!

Cannot be determined from the information given

No

Yes

No

Explanation:

One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute  in for . When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.

For our function:

Thus the function is not symmetric about the y-axis.

### Example Question #1 : Determine The Symmetry Of An Equation

Is the following function symmetric across the y-axis? (Is it an even function?)

There is not enough information to determine

I don't know!

No

That's not a function!

Yes

Yes

Explanation:

One way to determine algebraically if a function is an even function, or symmetric about the y-axis, is to substitute  in for . When we do this, if the function is equivalent to the original, then the function is an even function. If not, it is not an even function.

For our function:

Since this matches the original, our function is symmetric across the y-axis.

### Example Question #23 : Graphing Functions

Determine if there is symmetry with the equation  to the -axis and the method used to determine the answer.

Explanation:

In order to determine if there is symmetry about the x-axis, replace all  variables with .   Solving for , if the new equation is the same as the original equation, then there is symmetry with the x-axis.

Since the original and new equations are not equivalent, there is no symmetry with the x-axis.