## Quick Reference

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: 2*x*, *x*^{3}, *x*^{7}−8*x*^{3}+5*x*, 1/(*x*^{3}−*x*), sin *x*, tan *x*.

*Subjects:*
Mathematics.

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