Examples of even functions are ''x''<sup>2</sup>, ''x''<sup>4</sup>, [[trigonometric function|cos]](''x''), and [[hyperbolic function|cosh]](''x'').
==Odd functions==
Again, let ''f''(''x'') be a [[real number|real]] valued function of a real variable. Then ''f'' is '''odd''' if the following equation holds for all real ''x'':
:''f''(−''x'') = −''f''(''x'')
Geometrically, an odd function is symmetric with respect to rotation about the [[origin]].
The designation '''odd''' is due to the fact that the Taylor series of an odd function includes only odd powers.
Examples of odd functions are ''x'', ''x''<sup>3</sup>, [[trigonometric function|sin]](''x''), and [[hyperbolic function|sinh]](''x'').
