Are all functions either even functions or odd functions? Explain.

Question

make it simple and like a kid wrote it

Answer 1

No, not all functions are either even or odd!

An even function is one where if you plug in a number and then the negative of that number, you get the same answer. Like if you put in 2, and then -2, both will give you the same result. It looks like this: f(x) = f(-x).

An odd function is different. If you put in a number and then the negative of that number, you’ll get results that are opposite. So if you put in 2, and then -2, one will be positive and the other will be negative. It looks like this: f(-x) = -f(x).

But some functions don’t fit into either group. For example, the function f(x) = x + 1 isn't even because f(2) ≠ f(-2), and it isn't odd because f(-2) ≠ -f(2). So, there are functions that are not even and not odd!