Even and odd functions

In mathematics, an even function is a real function such that ${\displaystyle f(-x)=f(x)}$ for every ${\displaystyle x}$ in its domain. Similarly, an odd function is a function such that ${\displaystyle f(-x)=-f(x)}$ for every ${\displaystyle x}$ in its domain.

They are named for the parity of the powers of the power functions which satisfy each condition: the function ${\displaystyle f(x)=x^{n}}$ 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.