### All High School Math Resources

## Example Questions

### Example Question #1 : Finding Symmetries

This function is:

**Possible Answers:**

not symmetric

symmetric about the x-axis

symmetric about the origin

symmetric about the y-axis

**Correct answer:**

symmetric about the y-axis

Explanation:

A function's symmetry is related to its classification as even, odd, or neither.

**Even functions** obey the following rule:

Because of this, even functions are symmetric about the y-axis.

**Odd functions** obey the following rule:

Because of this, odd functions are symmetric about the origin.

If a function does not obey either rule, it is **neither** odd nor even. (A graph that is symmetric about the x-axis is not a function, because it does not pass the vertical line test.)

To test for symmetry, simply substitute into the original equation.

Thus, this equation is **even** and therefore symmetric about the y-axis.