# How do you test for symmetry with respect to the line y=-x?

##### 1 Answer

Dec 2, 2017

This function is symmetric with respect to the origin.

#### Explanation:

We have to test whether the function

When a function is even , it is symmetric with respect to the y-axis.

When a function is odd, it is symmetric with respect to the origin.

A function is even if

A function is odd if

A function could be neither odd nor even.

In this case, we replace

We ask ourselves:

Is this function even?

Therefore, no.

We ask ourselves:

Is this function odd?

Therefore, yes.

We now know that this function is odd, meaning that this function is symmetric with respect to the origin.