Graph of a function - Imported Knowlpedia Content

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

\Gamma_f=\{(a,f(a)):\ a\in A\}\subseteq A\times B.

Remarks

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 $\{(a,a):a\in A\}$ .