# Graph of a function

## Representation of a mathematical function / From Wikipedia, the free encyclopedia

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In mathematics, the **graph of a function** $f$ is the set of ordered pairs $(x,y)$, where $f(x)=y.$ In the common case where $x$ and $f(x)$ are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve.
The graphical representation of the graph of a function is also known as a *plot*.

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In the case of functions of two variables – that is, functions whose domain consists of pairs $(x,y)$ –, the graph usually refers to the set of ordered triples $(x,y,z)$ where $f(x,y)=z$. This is a subset of three-dimensional space; for a continuous real-valued function of two real variables, its graph forms a surface, which can be visualized as a *surface plot*.

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 does not 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.