= Graph of a function
{title2=$\operatorname{graph}(f)$}
{wiki}
= Graphs of functions
{synonym}
= Graphs of a function
{synonym}
= Function graph
{synonym}
For a <function> $f:A\to B$, its <graph of a function> is the <subset> $\{(x,f(x)):x\in A\}$ of the <Cartesian product> $A\times B$. Exactly one <ordered pair> has first coordinate $x$ for each $x\in A$. For example, the <quadratic function> $f(x)=x^2$ on the <real line> has the <parabola> as its graph.
The graph determines the values and the <domain of a function>, but alone does not record a larger specified <codomain>: the same <set> of <ordered pairs> can be regarded as lying in $A\times B$ or $A\times B'$ when both contain all its outputs. It also differs from a <graph> in <graph theory>, whose edges need not specify exactly one output per input.
Back to article page
