# Graph of a function

In mathematics, the graph of a function ${\displaystyle f}$ is the set of ordered pairs ${\displaystyle (x,y)}$, where ${\displaystyle f(x)=y.}$ In the common case where ${\displaystyle x}$ and ${\displaystyle f(x)}$ 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 ${\displaystyle (x,y),}$ the graph usually refers to the set of ordered triples ${\displaystyle (x,y,z)}$ where ${\displaystyle f(x,y)=z,}$ instead of the pairs ${\displaystyle ((x,y),z)}$ 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.