Odd Function

Author

Eric W. Weisstein
November 30, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/OddFunction.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/OddFunction.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Code

OddFunctionQ[f_]:=Module[{x},f[x]+f[-x]===0]

Examples

fs={#&,#^3&,Sin,Sinh,Tan,Tanh,Erf,FresnelC,FresnelS};

OddFunctionQ/@fs

Graphics

V5

<<Graphics`Colors`

Show[GraphicsArray[Partition[MapIndexed[Plot[#1,{x,-6,6},DisplayFunction->Identity,
AxesLabel->TraditionalForm/@{x,#1},PlotStyle->{Red,Orange,Yellow,Green,Blue,Indigo,Purple}[[#2[[1]]]]]&,Through[fs[x]]],4,4,{1,1},{}]],ImageSize->500]

V7

<<Graphics`Colors`;//Quiet

GraphicsGrid[Partition[MapIndexed[Plot[#,{x,-6,6},
AxesLabel->{x,#},Exclusions->If[#===Tan[x],Cot[x]==0,Automatic],PlotStyle->{Red,Orange,Yellow,Green,DarkGreen,Blue,Indigo,Violet,Purple}[[#2[[1]]]]]&,Through[fs[x]]],3,3,{1,1},{}],ImageSize->400,Spacings->{-20,10}]