is (x)/(x^2-9) an even or an odd function?
x / (x^2 - 9)
If a function is even, plugging in (-x) for (x) and then simplifying will yield the original function.
(-x) / ((-x)^2 - 9)
(-x) / (x^2 - 9)
That's not our original, so the function must be odd. (An odd function is the exact opposite of what you start with. In this case, we began with a positive function and ended up with a negative function.)