odd function

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The real function f is an odd function if f(−x)=−f(x) for all x (in the domain of f ). Thus the graph y=f(x) of an odd function is symmetrical about the origin; that is, it has a half-turn symmetry about the origin, because whenever (x, y) lies on the graph then so does (−x, −y). For example, f is an odd function when f(x) is defined as any of the following: 2x, x3, x7−8x3+5x, 1/(x3x), sin x, tan x.

Subjects: Mathematics.

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