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

1 Answer
Parabola
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(-x)=f(x)
A function is odd if f(-x)=-f(x)
A function could be neither odd nor even.
In this case, we replace y with f(x)
We ask ourselves:
Is this function even?
f(-x)=x and that is not equal to -x.
Therefore, no.

We ask ourselves:
Is this function odd?
f(-x)=x and that is equal to -f(x)=x.
Therefore, yes.

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

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