Graph of a function

A graph of a function is the set of input–output pairs: if $f:A\to B$ is a function , then its graph is

The graph is a subset of the Cartesian product and consists of ordered pairs . Viewing a function as a special kind of relation , the graph is exactly the corresponding relation.

Examples:

• If $f:\mathbb{R}\to\mathbb{R}$ is $f(x)=x^2$, then $\Gamma_f=\{(x,x^2):x\in\mathbb{R}\}$.
• If $A$ is any set, the graph of $\mathrm{id}_A$ is $\{(a,a):a\in A\}$.