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In mathematics, the graph of a function f {\displaystyle f} is the set of ordered pairs {\displaystyle } , where f = y . {\displaystyle f=y.} In the common case where x {\displaystyle x} and f {\displaystyle f} are 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 , {\displaystyle ,} the graph usually refers to the set of ordered triples {\displaystyle } where f = z , {\displaystyle f=z,} instead of the pairs , z ] {\displaystyle ,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.
A graph of a function is a special case of a relation.
In science, engineering, technology, finance, and other areas, graphs are tools used for many purposes. In the simplest case one variable is plotted as a function of another, typically using rectangular axes; see Plot for details.