information:extraction, stylistic:tone
Odd functions

A real function f is odd if, for every x in its domain, − x is also in its domain and f (− x) = − f (x) {\displaystyle f(-x)=-f(x)} or equivalently f (x) + f (− x) = 0. {\displaystyle f(x)+f(-x)=0.}

Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin.

If x = 0 {\displaystyle x=0} is in the domain of an odd function f (x) {\displaystyle f(x)}, then f (0) = 0 {\displaystyle f(0)=0}.

Examples of odd functions are: