math
posted by Anonymous on .
an equation is being tested for symmetry with respect to the xaxis, the yaxis, and the origin. explain why, if two of these symmetries are present then remaining one must also be present.

For xaxis reflection symmetry,
f(x,y) = f(x,y)
For yaxis reflection symmetry,
f(x,y) = f(x,y)
For symmetry about the origin,
f(x,y) = f(x,y)
If you reflect about both x and y axes, it is equivalent to reflecting about the origin.
If you reflect about the origin and then one axis, you have reflected about the other axis.