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Encyclopedia > Graphs of functions

In mathematics, the graph of a function f is the collection of all ordered pairs (x,f(x)). In particular, graph means the graphical representation of this collection, in the form of a curve or surface, together with axes, etc. Graphing on a Cartesian plane is sometimes referred to as curve sketching. Partial plot of a function f. ... In mathematics, an ordered pair is a collection of two objects such that one can be distinguished as the first element and the other as the second element (the first and second elements are also known as left and right projections). ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... An open surface with X-, Y-, and Z-contours shown. ... Fig. ...


The graph of the function

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


The graph of the cubic polynomial on the real line

f(x) = x3 − 9x

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


Image File history File links Cubicpoly. ...


Therefore 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 in terms of the operator graph. ... Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of spaces of functions. ...


The concept of the graph of a function is generalised to the graph of a relation. 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. 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 finitary relation is defined by one of the formal definitions given below. ... A codomain in mathematics is the set of output values associated with (or mapped to) the domain of inputs in a function. ... A surjective function. ... In mathematics, the set of real numbers, denoted R, or in blackboard bold , is the set of all rational and irrational numbers. ... In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = −1. ...

Contents

Tools for plotting function graphs

Hardware

Hardware is the general term that is used to describe physical artifacts of a technology. ... A graphing calculator is a special kind of scientific/engineering calculator that is able to display and/or analyze mathematical function graphs. ... A Tektronix model 475A portable analogue oscilloscope, a very typical instrument of the late 1970s. ...

Software

See List of graphing software Computer software (or simply software) refers to one or more computer programs and data held in the storage of a computer for some purpose. ... This is an incomplete list of software that either includes the ability to create one or more infographics from a provided data set, or is provided specifically for information visualization. ...


See also


  Results from FactBites:
 
Graph - Wikipedia, the free encyclopedia (153 words)
In graph theory, a graph is an abstract object consisting of vertices (or nodes) and edges (or arcs) between pairs of vertices.
The graph of a relation, a generalisation of the graph of a function.
In computer science, a graph is a data structure representing mathematical graphs.
  More results at FactBites »

 
 

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