Graph of a function

See also: Graph

In Set theory, the graph of a function or graph ensemblist G of a correspondence $\ mathfrak {C} \,$ whose starting whole is called E and the whole of arrival F , is the Sous-ensemble of E × F formed by the couple S of elements bound by the correspondence:

G = \ {(X, there) \ in E \ times F \,|\, X \ mathfrak {C} there \, \} \,

The unit G is called graph $\ mathfrak {C}$ because it makes it possible to give a chart of it: indeed, if one can represent E and F on two secant axes, each couple of G can then be represented by a point in the plan defined by the two axes. For example, a numerical Fonction (of $\ mathbb {R}$ in $\ mathbb {R}$ ) can be represented by a plane curve; one also speaks about curve représentatrice of the function.

Note: if the correspondence is a function whose starting whole is a Cartesian square , it is preferable to represent E like a plan and not an axis. In this case, the function is represented by a left surface in usual space with 3 dimensions.

It is possible then to be brought back to a plane representation by considering level line , i.e. by drawing in the starting plan a altimetric Carte of the Relief of left surface.

See too

External bonds

FooPlot - to trace graphs for mathematical functions in 2D and 3D

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Graph of a function

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