Definition:Graph of Mapping

Let $$f: S \to T$$ be a mapping.

Then the relation $$\mathcal{R} \subseteq S \times T$$ defined as $$\mathcal{R} = \left\{{\left({x, f \left({x}\right)}\right): x \in S}\right\}$$ is called the graph of $$f$$.

The word is usually used in the context of a diagram:



The defining nature of a mapping means that each vertical line through a point in $$A$$ intersects the graph at one and only one place, corresponding to a single point in $$B$$.

Note
Not to be confused with a graph theoretic graph.