How do you know if a function is odd or even?

For this I would use the whiteboard to draw an even function (i.e cos(x)) and show that if f(x) is even then f(x) = f(-x). I would also show that the function would be symmetrical about the y axis. For an odd function I would show that f(-x) = -f(x) and demonstrate this graphically (e.g with sin(x)). While still relevant to the question I would also show that there are functions which can be neither odd nor even following the previous logic.