There are three tests for symmetry.

1. Symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with -y. Everywhere you see y, plug in a -y. Then see if the equation is still the same.

2. Symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with -x.

3. 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.

y = 4x/(x+2)^2 - test for symmetry about x-axis. Replace y with -y:

-y = 4x/(x+2)^2 divide everything by -1 to get y by itself.

y = -4x/(x+2)^2 The equation is not the same, so there is no symmetry about the x-axis.

Now you test 2 and 3.