information:classification, structural:reformatting
Specifying a function

Given a function f {\displaystyle f}, by definition, to each element x {\displaystyle x} of the domain of the function f {\displaystyle f}, there is a unique element associated to it, the value f (x) {\displaystyle f(x)} of f {\displaystyle f} at x {\displaystyle x}. There are several ways to specify or describe how x {\displaystyle x} is related to f (x) {\displaystyle f(x)}, both explicitly and implicitly. Sometimes, a theorem or an axiom asserts the existence of a function having some properties, without describing it more precisely. Often, the specification or description is referred to as the definition of the function f {\displaystyle f}.