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 → 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

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

The graph of the cubic polynomial on the real line

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

Tools for plotting function graphs

Hardware

• Graphing calculator
• Oscilloscope

Software

See List of graphing software

See also

External links

• Some Java applets to study Real Functions
• Weisstein, Eric W. Hardware is a general term that refers to the physical artifacts of a Technology. A graphing calculator (also known as a graphic calculator or graphical calculator) typically refers to a class of handheld Calculators that are capable of An oscilloscope (commonly abbreviated to scope or O-scope) is a type of Electronic test equipment that allows signal Voltages to be viewed This is a list of software to create any kind of Information graphics: either includes the ability to create one or more Infographics from a provided data set In Mathematics, a critical point (or critical number) is a point on the domain of a function where one dimension In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Mathematics, the epigraph of a function f    R n→ R is the set of points lying on or above its A chart or graph is a type of Information graphic, that represents tabular numeric data and/or functions. In Mathematics, particularly in Calculus, a stationary point is an input to a function where the Derivative is zero (equivalently the Slope is used to describe the steepness incline gradient or grade of a straight line. An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent A tetraview is an attempt to graph a Complex function of a Complex variable, by a method invented by Davide P A three-dimensional graph is the graph of a function of two Variables f ( x, y) In function graphing, a vertical translation is a related graph which for every point ( x, y) has a y value In Coordinate geometry, the y -intercept is the y-value of the point where the Graph of a function or relation intercepts the y -axis "Function Graph. " From MathWorld--A Wolfram Web Resource.