Editing Even and odd functions (section)

===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 =block>f(-x) = -f(x)</math>
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.

If <math>x=0</math> is in the domain of an odd function <math>f(x)</math>, then <math>f(0)=0</math>.

Examples of odd functions are:
*The [[sign function]] <math>x \mapsto \sgn(x),</math>
*The identity function <math>x \mapsto x,</math>
*<math>x \mapsto x^n</math> for any odd integer <math>n,</math>
*<math>x \mapsto \sqrt[n]{x}</math> for any odd positive integer <math>n,</math>
*[[sine]] <math>\sin,</math>
*[[hyperbolic function|hyperbolic sine]] <math>\sinh,</math>
*The [[error function]] <math>\operatorname{erf}.</math>

[[Image:Function-x3plus1.svg|right|thumb|<math>f(x)=x^3+1</math> is neither even nor odd.]]