graph (idea)

If f is a function from X to Y, then the set G := { (x,y) | y=f(x) for all f(x) } is said to be the graph of f.
If f is a function from some subset D of R to R, the set G, consisting of ordered pairs of real numbers, can be depicted visually on the coordinate plane.

Take note that the mathematical definition of the graph of a function does not rely on a "graphical" representation of the function, whereas one common definition does.