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→Even functions: If the ___domain consists only of positive numbers, the function is not said to be even |
→Odd functions: If the ___domain contains only positive numbers, the function is not odd |
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===Odd functions===
[[Image:Function-x3.svg|right|thumb|<math>f(x)=x^3</math> is an example of an odd function.]]
A real function {{math|''f''}} is '''odd''' if, for every {{mvar|x}} in its ___domain, {{math|−''x''}} is also in its ___domain and<ref name=FunctionsAndGraphs/>{{rp|p. 72}}
<math display
or equivalently
<math display =block>f(x) + f(-x) = 0.</math>
Geometrically, the graph of an odd function has rotational symmetry with respect to the [[Origin (mathematics)|origin]], meaning that its graph remains unchanged after [[Rotation (mathematics)|rotation]] of 180 [[Degree (angle)|degree]]s about the origin.
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