Graph of a function: Difference between revisions

Revision as of 01:07, 13 June 2003

Revision as of 07:18, 13 June 2003

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[[Image::cubicpoly.png]]

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 [[Closeclosed graph theorem]] in [[functional analysis]].

The concept of the graph of a function is generalised to the graph of a [[relation]]. Note that althrough a function is always identified with its graph, they are not the same because it will happen 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]].