In mathematics, an even function is a real function such that for every in its domain. Similarly, an odd function is a function such that for every in its domain.
They are named for the parity of the powers of the power functions which satisfy each condition: the function is even if n is an even integer, and it is odd if n is an odd integer.
Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the origin.
If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an odd function.