Graph of a function: Difference between revisions

Revision as of 15:14, 23 April 2004

Revision as of 13:53, 13 May 2004

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[[eo:Grafeo]] [[de:Funktionsgraph]] [[ja:グラフ]]

[[eo:Grafeo]]

[[fr:Graphe]]

[[ja:グラフ]]

Mathematically, the '''graph''' of a [[function (mathematics)|function]] is the collection of all pairs (''x'', ''f''(''x'')) of the function. In particular ''graph'' means the graphical representation of this collection, in the form of a curve, together with axes, etc. Graphing is sometimes referred to as '''curve sketching'''.

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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 althroughalthough 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]].

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