Pre-Calc Help please!!!?

Question

Here is the problem:

Use the algebraic tests to check for symmetry with respect to both axes and the orgin.

x - y^2 = 0

Please show step by step if you can, thanks!

Answer 1

Tests for symmetry:

1.  A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with -y.

2.  A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with -x.

3.  A graph will have symmetry about the origin if we get an equivalent equation when all the y’s are replaced with -y and all the x’s are replaced with -x.

If you perform those tests, you will see that this equation is symmetric to the x-axis and the origin.