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

Dec 2, 2017

This function is symmetric with respect to the origin.

#### Explanation:

We have to test whether the function $y = - x$ is even or odd.
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 $f \left(- x\right) = f \left(x\right)$
A function is odd if $f \left(- x\right) = - f \left(x\right)$
A function could be neither odd nor even.
In this case, we replace $y$ with $f \left(x\right)$
$f \left(- x\right) = x$ and that is not equal to $- x$.
$f \left(- x\right) = x$ and that is equal to $- f \left(x\right) = x$.