# Graph of a function

In mathematics, the **graph of a function** is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

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In the case of functions of two variables, that is functions whose domain consists of pairs the graph usually refers to the set of ordered triples where instead of the pairs 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.

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 (graphics)* for details.

A graph of a function is a special case of a relation.
In the modern foundations of mathematics, and, typically, in set theory, a function is actually equal to its graph.[1] However, it is often useful to see functions as mappings,[2] which consist not only of the relation between input and output, but also which set is the domain, and which set is the codomain. For example, to say that a function is onto (surjective) or not the codomain should be taken into account. The graph of a function on its own doesn't determine the codomain. It is common[3] to use both terms *function* and *graph of a function* since even if considered the same object, they indicate viewing it from a different perspective.