Graph of a function: Difference between revisions

Revision as of 17:50, 8 February 2021

Revision as of 18:53, 8 February 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''}} is defined as the set of [[ordered pair]]s {{math|(''x'', ''y'')}}, where {{math|''f''(''x'') {{=}} ''y''}}. In the common case where {{mvar|x}} and {{math| ''f''(''x'')}} 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 consists of pairs {{math|(''x'', ''y'')}}, the graph usually refers to the set of [[ordered triple]]s {{math|(''x'', ''y'', ''z'')}} where {{math|''f''(''x'', ''y'') {{=}} ''z''}}, instead of the pairs {{math|((''x'', ''y''), ''z'')}} 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]].