a function is even if f(x) = f(-x). that is, if you replace x with -x and simplify, you get exactly the original function

a function is odd if f(-x) = -f(x). that is, if you replace x with -x and simplify, you get the negative of the original function

see the "Ways to test for symmetry" section here on how to test for other kinds of symmetry. i don't know what kinds you are expected to look for.

note: symmetry about the y-axis is the same as being even, and symmetry about the origin is the same as being odd