Question

How do you determine whether the graph of `y=1/x^2` is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?

Answer 1

`y` is symmetric about the `y-`axis

Explanation:

`y=1/x^2`

The graph below shows `y` with respect to the primary axes and `y=+-x`

graph{(y-(1/x^2))(y-x)(y+x)=0 [-14.24, 14.23, -7.12, 7.11]}

From which we can see that `y` has "mirror" symmetry about the `y-`axis.