Analysis of Functions? Symmetry?

Question

I need to know how to determine whether each equation is symetric with respec to the x-axis the y-axis the line y=x and the line y= -x.
FOR Y= 1/x^2
If you dont know the formulas they are
x-axis= f(x)= -f(x)
y-axis= f(x)= f(-x)
y=x = (x, f(x) ) <-> ( f(x), x)
y=-x = (x, f(x) ) -> (-f(x), -x)

I need step by step directions i have a test tomorrow

Answer 1

f(-x) = 1/(-x)^2 = 1/x^2 = f(x) so the function is symmetric to the y-axis

-f(x) = -1/x^2 <> 1/x^2 so not symmetric to x-axis

The function is not symmetric to the line y=x or y=-x because its inverse is not a function.

Answer 2

do your own work