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

Question

3599 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-24T16:29:26

Symmetrical about both x and y axes.

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.

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