When do you use even odd and neither functions?

You use an even function if f(-x) = f(x) for all x.You use an odd function if f(-x) = -f(x) for all x.

and you use neither if there is at least one point for which one or the other of the above is not true.

Most functions are neither even nor odd.

Basically, a knowledge of even and odd functions can simplify certain calculations. One place where they frequently appear is when using trigonometric functions - for example, the sine function is odd, while the cosine function is even.