Function

Function may refer to:

Math, computing and engineering

Function (mathematics), a relation that associates an input to a single output according to some rule

Function model, a structured representation of the functions, activities or processes

Function (engineering), related to the selected property of a system

Subroutine, also called a function, a sequence of instructions within a larger computer program

Function object, or functor or functionoid, a concept of object-oriented programming

Music

Diatonic function, a term in music theory

"Function" (song), a 2012 song by American rapper E-40 featuring YG, Iamsu! & Problem

"Function", song by Dana Kletter from Boneyard Beach (Dish album) 1995

Other uses

A social event

Function (biology), explaining why a feature survived selection

Function (language), in linguistics, a way of achieving an aim using language

Function Drinks, a beverage company based in Redondo Beach, California.

Minkowski's question mark function

In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by $?(x)$ , is a function possessing various unusual fractal properties, defined by Hermann Minkowski (1904, pages 171–172). It maps quadratic irrationals to rational numbers on the unit interval, via an expression relating the continued fraction expansions of the quadratics to the binary expansions of the rationals, given by Arnaud Denjoy in 1938. In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern–Brocot tree.

Definition

If $[a_0; a_1, a_2, \ldots]$ is the continued fraction representation of an irrational number $x$ , then

whereas:

If $[a_0; a_1, a_2, \ldots, a_m]$ is a continued fraction representation of a rational number $x$ , then

Intuitive explanation

To get some intuition for the definition above, consider the different ways of interpreting an infinite string of bits beginning with 0 as a real number in $[0,1]$ . One obvious way to interpret such a string is to place a binary point after the first 0 and read the string as a binary expansion: thus, for instance, the string 001001001001001001001001... represents the binary number 0.010010010010..., or $2/7$ . Another interpretation views a string as the continued fraction $[0; a 1, a 2, \dots ]$ , where the integers $a i$ are the run lengths in a run-length encoding of the string. The same example string 001001001001001001001001... then corresponds to $[0; 2, 1, 2, 1, 2, 1, \dots] =$ √3 − 1/2. If the string ends in an infinitely long run of the same bit, we ignore it and terminate the representation; this is suggested by the formal "identity":

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Minkowski's_question_mark_function

Function (mathematics)

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. Likewise, if the input is 3, then the output is also 9, and we may write f(3) = 9. (The same output may be produced by more than one input, but each input gives only one output.) 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.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Function_(mathematics)

Derivative

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time is advanced.

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

Derivatives may be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables. It can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Derivative

FX

FX, F-X, F/X, Fx, or fx may refer to:

Arts, media, and entertainment

(See also below: Arts, media, and entertainment technology)

Film and television

FX (TV channel), an international cable/satellite television network (see article for channels by country)

F/X (1986, also known as or subtitled Murder by Illusion), an American action-thriller film set in the world of special effects

F/X: The Series, a television program based on the movie

F/X: The Series, a television program based on the movie

Music

f(x) (band), South Korean girl group

"FX", a song on Vol. 4 (Black Sabbath album)

HfsNegative FX, hardcore band from Cg Boston

Print

FX (comics), a comic book series published by IDW, drawn by artist John Byrne

FX (magazine), a UK trade magazine

Medicine

Bone fracture, in medical shorthand

Factor X, a protein involved in coagulation

Technology

Athlon 64 FX, a variant of the AMD Athlon 64 microprocessor

dotNetFx, the Microsoft .NET Framework

Foreign exchange service (telecommunications), a telephone connection to a distant exchange

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/FX

FX

FX, F-X, F/X, Fx, or fx may refer to:

Arts, media, and entertainment

(See also below: Arts, media, and entertainment technology)

Film and television

FX (TV channel), an international cable/satellite television network (see article for channels by country)

F/X (1986, also known as or subtitled Murder by Illusion), an American action-thriller film set in the world of special effects

F/X: The Series, a television program based on the movie

F/X: The Series, a television program based on the movie

Music

f(x) (band), South Korean girl group

"FX", a song on Vol. 4 (Black Sabbath album)

HfsNegative FX, hardcore band from Cg Boston

Print

FX (comics), a comic book series published by IDW, drawn by artist John Byrne

FX (magazine), a UK trade magazine

Medicine

Bone fracture, in medical shorthand

Factor X, a protein involved in coagulation

Technology

Athlon 64 FX, a variant of the AMD Athlon 64 microprocessor

dotNetFx, the Microsoft .NET Framework

Foreign exchange service (telecommunications), a telephone connection to a distant exchange

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/F_X

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Function

Function may refer to:

Math, computing and engineering

Function (mathematics), a relation that associates an input to a single output according to some rule

Function model, a structured representation of the functions, activities or processes

Function (engineering), related to the selected property of a system

Subroutine, also called a function, a sequence of instructions within a larger computer program

Function object, or functor or functionoid, a concept of object-oriented programming

Music

Diatonic function, a term in music theory

"Function" (song), a 2012 song by American rapper E-40 featuring YG, Iamsu! & Problem

"Function", song by Dana Kletter from Boneyard Beach (Dish album) 1995

Other uses

A social event

Function (biology), explaining why a feature survived selection

Function (language), in linguistics, a way of achieving an aim using language

Function Drinks, a beverage company based in Redondo Beach, California.

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Function

Math, computing and engineering

Music

Other uses

See also

Minkowski's question mark function

Definition

Intuitive explanation

Function (mathematics)

Derivative

FX

Arts, media, and entertainment

Film and television

Music

Print

Medicine

Technology

FX

Arts, media, and entertainment

Film and television

Music

Print

Medicine

Technology

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