Question

How do you determine whether the graph of `y^2=x^2` is symmetric with respect to the x axis, y axis or neither?

Answer 1

Symmetrical about both x and y axes.

Explanation:

For symmetry about the y axis, see if `y(x) = y(-x)`

Here you have:

`y = pm sqrt(x^2) = pm abs x`.

So `y(-x) = pm abs (-x) = pm abs x`. Looks symmetrical about the y axis.

Likewise, for symmetry about the x axis, see if `x(y) = x(-y)`.

In this case:

`x = pm sqrt(y^2) = pm abs y`. So `x(-y) = pm abs (-y) = pm abs y`. Looks symmetrical about the x axis.