Graph of a function: Difference between revisions

Revision as of 12:20, 14 February 2005

Revision as of 15:58, 21 February 2005

Line 13:

Therefore the graph of a function on real numbers is identical to the graphic representation of the function. For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e.g., the [[closed graph theorem]] in [[functional analysis]].

The concept of the graph of a function is generalised to the graph of a [[relation (mathematics)|relation]]. Note that although a function is always identified with its graph, they are not the same because it will happen that two functions with different [[codomain]] could have the same graph. For example, the cubic polynomial mentioned above is a [[surjection]] if its codomain is the [[real number]]s but it is not if its codomain is the [[complex number|complex field]].

==See also==