In mathematics, the graph of a function f is the collection of all ordered pairs (x,f(x)). The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function In Mathematics, an ordered pair is a collection of two distinguishable objects one of which is identified as the first coordinate (or the first entry In particular, graph means the graphical representation of this collection, in the form of a curve or surface, together with axes, etc. In Mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object In Mathematics, specifically in Topology, a surface is a Two-dimensional Manifold. Graphing on a Cartesian plane is sometimes referred to as curve sketching. In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane

The graph of a function on real numbers is identical to the graphic representation of the function. For general functions, the graphic representation cannot be applied 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. In Mathematics, the closed graph theorem is a basic result in Functional analysis which characterizes Continuous linear operators between Banach spaces For functional analysis as used in psychology see the Functional analysis (psychology article

The concept of the graph of a function is generalised to the graph of a relation. This article sets out the set-theoretic notion of relation For a more elementary point of view see Binary relations and Triadic relations Note that although a function is always identified with its graph, they are not the same because it will happen that two functions with different codomain could have the same graph. In Mathematics, the codomain, or target, of a function f: X ā Y is the set For example, the cubic polynomial mentioned above is a surjection if its codomain is the real numbers but it is not if its codomain is the complex field. In Mathematics, a function f is said to be surjective or onto, if its values span its whole Codomain; that is for every In Mathematics, the real numbers may be described informally in several different ways Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted

## Examples

The graph of the function

$f(x)=\left\{\begin{matrix} a, & \mbox{if }x=1 \\ d, & \mbox{if }x=2 \\ c, & \mbox{if }x=3. \end{matrix}\right.$

is {(1,a), (2,d), (3,c)}.

The graph of the cubic polynomial on the real line

$f(x)={{x^3}-9x} \!\$

is {(x,x3-9x) : x is a real number}. If the set is plotted on a Cartesian plane, the result is