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?

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Answer 1 · 2018-05-23T13:07:48

$y$ is symmetric about the $y-$ axis

$y=1/x^2$

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.

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