Graph of a function: Difference between revisions

Revision as of 18:53, 8 February 2021

Revision as of 04:23, 2 May 2021

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[[File:F(x) = x^3 − 9x.PNG|right|thumb|250px| Graph of the function {{nowrap|1=''f''(''x'') = ''x''³ − 9''x''}}]]

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 {{mvar|<math>x}}</math> and {{<math| ''>f''(''x'')}}</math> are [[real number|real numbers]], 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'')}}, 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]].

{{anchor|graph of a relation}}