Even and odd functions: Difference between revisions

Revision as of 20:06, 24 October 2004

Revision as of 02:27, 26 October 2004

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Let ''f''(''x'') be a [[real number|real]]-valued function of a real variable. Then ''f'' is '''even''' if the following equation holds for all real ''x'':

:''f''(-−''x'') = ''f''(''x'')

Geometrically, an even function is [[symmetry|symmetric]] with respect to the ''y''-axis.

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Again, let ''f''(''x'') be a 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 the [[origin]].