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

1 Answer
Jan 24, 2017

Answer:

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.