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• Function_(mathematics) abstract "In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.Functions of various kinds are "the central objects of investigation" in most fields of modern mathematics. There are many ways to describe or represent a function. Some functions may be defined by a formula or algorithm that tells how to compute the output for a given input. Others are given by a picture, called the graph of the function. In science, functions are sometimes defined by a table that gives the outputs for selected inputs. A function could be described implicitly, for example as the inverse to another function or as a solution of a differential equation.The input and output of a function can be expressed as an ordered pair, ordered so that the first element is the input (or tuple of inputs, if the function takes more than one input), and the second is the output. In the example above, f(x) = x2, we have the ordered pair (−3, 9). If both input and output are real numbers, this ordered pair can be viewed as the Cartesian coordinates of a point on the graph of the function. But no picture can exactly define every point in an infinite set.In modern mathematics, a function is defined by its set of inputs, called the domain; a set containing the set of outputs, and possibly additional elements, as members, called its codomain; and the set of all input-output pairs, called its graph. (Sometimes the codomain is called the function's "range", but warning: the word "range" is sometimes used to mean, instead, specifically the set of outputs. An unambiguous word for the latter meaning is the function's "image". To avoid ambiguity, the words "codomain" and "image" are the preferred language for their concepts.) For example, we could define a function using the rule f(x) = x2 by saying that the domain and codomain are the real numbers, and that the graph consists of all pairs of real numbers (x, x2). Collections of functions with the same domain and the same codomain are called function spaces, the properties of which are studied in such mathematical disciplines as real analysis, complex analysis, and functional analysis.In analogy with arithmetic, it is possible to define addition, subtraction, multiplication, and division of functions, in those cases where the output is a number. Another important operation defined on functions is function composition, where the output from one function becomes the input to another function.".
• Function_(mathematics) thumbnail Function_machine2.svg?width=300.
• Function_(mathematics) wikiPageExternalLink visual.calculus.
• Function_(mathematics) wikiPageExternalLink books?id=7JKVu_9InRUC.
• Function_(mathematics) wikiPageExternalLink books?id=B3WvWhJTTX8C&pg=PA468.
• Function_(mathematics) wikiPageExternalLink books?id=QJ_537n8zKYC.
• Function_(mathematics) wikiPageExternalLink books?id=x6cZBQ9qtgoC.
• Function_(mathematics) wikiPageExternalLink functions.wolfram.com.
• Function_(mathematics) wikiPageExternalLink xFunctions.
• Function_(mathematics) wikiPageExternalLink function-graphs.
• Function_(mathematics) wikiPageExternalLink fcn_graph_eval.php.
• Function_(mathematics) wikiPageExternalLink MMFunctions.htm.
• Function_(mathematics) wikiPageExternalLink cartesian.htm.
• Function_(mathematics) wikiPageExternalLink FunctionMain.shtml.
• Function_(mathematics) wikiPageExternalLink BookOfProof.
• Function_(mathematics) wikiPageExternalLink Functions.pdf.
• Function_(mathematics) wikiPageExternalLink FunctionFlyer.
• Function_(mathematics) wikiPageExternalLink algebra-functions.
• Function_(mathematics) wikiPageID "185427".
• Function_(mathematics) wikiPageRevisionID "606078028".
• Function_(mathematics) align "right".
• Function_(mathematics) caption "However, this second diagram does not represent a function. One reason is that 2 is the first element in more than one ordered pair. In particular, and are both elements of the set of ordered pairs. Another reason, sufficient by itself, is that 3 is not the first element for any ordered pair. A third reason, likewise, is that 4 is not the first element of any ordered pair.".
• Function_(mathematics) caption "The above diagram represents a function with domain , codomain and set of ordered pairs . The image is .".
• Function_(mathematics) direction "vertical".
• Function_(mathematics) hasPhotoCollection Function_(mathematics).
• Function_(mathematics) id "Function".
• Function_(mathematics) id "p/f041940".
• Function_(mathematics) image "Injection keine Injektion 1.svg".
• Function_(mathematics) image "Injection keine Injektion 2a.svg".
• Function_(mathematics) title "Function".
• Function_(mathematics) subject Category:Basic_concepts_in_set_theory.
• Function_(mathematics) subject Category:Elementary_mathematics.
• Function_(mathematics) subject Category:Functions_and_mappings.
• Function_(mathematics) type Abstraction100002137.
• Function_(mathematics) type BasicConceptsInSetTheory.
• Function_(mathematics) type Cognition100023271.
• Function_(mathematics) type Concept105835747.
• Function_(mathematics) type Content105809192.
• Function_(mathematics) type Function113783816.
• Function_(mathematics) type FunctionsAndMappings.
• Function_(mathematics) type Idea105833840.
• Function_(mathematics) type MathematicalRelation113783581.
• Function_(mathematics) type PsychologicalFeature100023100.
• Function_(mathematics) type Relation100031921.
• Function_(mathematics) comment "In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9.".
• Function_(mathematics) label "Fonction (mathématiques)".
• Function_(mathematics) label "Función matemática".
• Function_(mathematics) label "Functie (wiskunde)".
• Function_(mathematics) label "Function (mathematics)".
• Function_(mathematics) label "Funkcja".
• Function_(mathematics) label "Funktion (Mathematik)".
• Function_(mathematics) label "Funzione (matematica)".
• Function_(mathematics) label "Função (matemática)".
• Function_(mathematics) label "Функция (математика)".
• Function_(mathematics) label "دالة (رياضيات)".
• Function_(mathematics) label "函数".
• Function_(mathematics) label "関数 (数学)".
• Function_(mathematics) sameAs Funkce_(matematika).
• Function_(mathematics) sameAs Funktion_(Mathematik).
• Function_(mathematics) sameAs Συνάρτηση.
• Function_(mathematics) sameAs Función_matemática.
• Function_(mathematics) sameAs Funtzio_(matematika).
• Function_(mathematics) sameAs Fonction_(mathématiques).
• Function_(mathematics) sameAs Fungsi_(matematika).
• Function_(mathematics) sameAs Funzione_(matematica).
• Function_(mathematics) sameAs 関数_(数学).
• Function_(mathematics) sameAs 함수.
• Function_(mathematics) sameAs Functie_(wiskunde).
• Function_(mathematics) sameAs Funkcja.
• Function_(mathematics) sameAs Função_(matemática).
• Function_(mathematics) sameAs m.02v_93z.
• Function_(mathematics) sameAs Q11348.
• Function_(mathematics) sameAs Q11348.
• Function_(mathematics) sameAs Function_(mathematics).
• Function_(mathematics) wasDerivedFrom Function_(mathematics)?oldid=606078028.
• Function_(mathematics) depiction Function_machine2.svg.
• Function_(mathematics) isPrimaryTopicOf Function_(mathematics).