Graph of a function: Difference between revisions

Revision as of 16:48, 21 October 2023

Revision as of 15:54, 24 October 2023

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{{Short description|Mathematical representation of a function}}

{{for -multi|graphical representation|Plot (graphics)|the combinatorial structure|Graph (discrete mathematics)|the graph-theoretic representation of a function from a set to itself|Functional graph}}

{{refimprovemore citations needed|date=August 2014}}{{functions}}

[[File:Polynomial of degree three.svg|thumb|250x250px|Graph of the function <math>f(x)=\frac{x^3+3x^2-6x-8}{4}.</math>]]

In [[mathematics]], the '''graph of a [[Function (mathematics)|function]]''' <math>f</math> is the set of [[ordered pair]]s <math>(x, y)</math>, where <math>f(x) = y.</math> In the common case where <math>x</math> and <math>f(x)</math> are [[real number]]s, these pairs are [[Cartesian coordinates]] of points in [[two-dimensional space]] and thus form a subset of this plane.

In the case of functions of two variables, that is functions whose [[Domain of a function|___domain]] consists of pairs <math>(x, y),</math> the graph usually refers to the set of [[ordered triple]]s <math>(x, y, z)</math> where <math>f(x,y) = z,</math> instead of the pairs <math>((x, y), z)</math> as in the definition above. This set is a subset of [[three-dimensional space]]; for a continuous [[real-valued function]] of two real variables, it is a [[Surface (mathematics)|surface]].

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{{Calculus topics}}

{{Visualization}}

{{Authority control}}

[[Category:Charts]]