An odd function is defined by

. An even function is defined by

Since

**and** the function is neither odd nor even...

A function is odd if it fulfills the condition

, and even if it fulfils

. If it fulfills neither condition, then it is neither.

In other words. If you have a graph of an odd function, then if you pick ANY value of x, and note the value of f(x). Then go to the -x on the same graph, you should find that the value is negative the value of the f(x) you noted earlier. (see sin(x))

And for the graph of an even function, if you pick ANY value of x, and note the value of y=f(x), then go to -x on the same graph, you should find that the y value is the same as it was for positive x. (see cos(x))

For a function which is neither, you will not be able to do this for

**all** values of x.