Graph of a function
In mathematics, the graph of a function f is the collection of all ordered pairs (x, f(x)). If the function input x is a scalar, the graph is a two-dimensional graph, and for a continuous function is a curve. If the function input x is an ordered pair (x1, x2) of real numbers, the graph is the collection of all ordered triples (x1, x2, f(x1, x2)), and for a continuous function is a surface (see three-dimensional graph).
Informally, if x is a real number and f is a real function, graph may mean the graphical representation of this collection, in the form of a line chart: a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is sometimes referred to as curve sketching. The graph of a function on real numbers may be mapped directly to the graphic representation of the function. For general functions, a graphic representation cannot necessarily be found and the formal definition of the graph of a function suits the need of mathematical statements, e.g., the closed graph theorem in functional analysis.
