Editing Even and odd functions (section)

{{Short description|Functions such that f(–x) equals f(x) or –f(x)}}
{{distinguish|Even and odd numbers}}
[[File:Sintay SVG.svg|thumb|The [[sine function]] and all of its [[Taylor polynomial]]s are odd functions.]]
[[File:Développement limité du cosinus.svg|thumb|The [[cosine function]] and all of its [[Taylor polynomials]] are even functions.]]

In [[mathematics]],  an '''even function''' is a [[real function]] such that <math>f(-x)=f(x)</math> for every <math>x</math> in its [[domain of a function|domain]]. Similarly, an '''odd function''' is a function such that <math>f(-x)=-f(x)</math> for every <math>x</math> in its domain.

They are named for the [[parity (mathematics)|parity]] of the powers of the [[Power Function|power functions]] which satisfy each condition: the function <math>f(x) = x^n</math> 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 of a function|graph]] is [[symmetry (geometry)|self-symmetric]] with respect to the {{nowrap|{{mvar|y}}-axis,}} and odd functions are those whose graph is self-symmetric with respect to the [[origin (mathematics)|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.