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https://en.wikipedia.org/wiki/Function_(mathematics)

-Kamen

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The evolution of the concept of function goes back 4000 years; 3,700 of these consist of anticipations. The idea evolved for close to 300 years in intimate connection with problems in calculus and analysis. In fact, a one-sentence definition of analysis as the study of properties of various classes of functions would not be far off the mark. Moreover, the concept of function is one of the distinguishing features of “modern” as against “classical” mathematics.

-Kamen

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-Kamen

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https://www.brightstorm.com/math/algebra-2/functions/introduction-to-functions/

-by Becky

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Such as
"(bx+c)

-by Becky

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a relationship or expression involving one or more variables

-by Becky

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ex. f(x)=x² : an input of 4, becomes an output of 16, so we can write f(4)=16
-Jena

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The input
The relationship
The output
-Jena

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Function is a relation or expression involving one or more variables.

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Function is a relation or expression involving one or more variables.

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-Jena

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In the 18th and 19th centuries, scientists discovered that the elementary functions--powers, roots, trigonometric functions and their inverses--had their limitations. They found that solutions for some important physical problems--like the orbital motion of planets, the oscillatory motion of suspended chains, and the calculation of the gravitational potential of nearly spherical bodies--could not always be described in a closed form using only elementary functions.

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A function is a rule which relates the values of one variable quantity to the values of another variable quantity, and does so in such a way that the value of the second variable quantity is uniquely determined by (i.e. is a function of) the value of the first variable quantity.
- Polly

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By Buster

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By Buster

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Here is the video
https://www.khanacademy.org/math/algebra/algebra-functions/evaluating-functions/v/what-is-a-function

Julian

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This is not the mathematical description of a function..
Search it again!!

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In order to avoid the use of the informally defined concepts of "rules" and "associates", the above intuitive explanation of functions is completed with a formal definition. This definition relies on the notion of the Cartesian product. The Cartesian product of two sets X and Y is the set of all ordered pairs, written (x, y), where x is an element of X and y is an element of Y. The x and the y are called the components of the ordered pair. The Cartesian product of X and Y is denoted by X × Y.
---Christina

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Functions before the 17th century. According to DieudonnÃ© and Ponte, the concept of a function emerged in the 17th century as a result of the development of analytic geometry and the infinitesimal calculus. Nevertheless, Medvedev suggests that the implicit concept of a function is one with an ancient
lineage.
by Vitor

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Function Machine Division: If you think the numbers are being divided by 2, simply enter ÷2.
While there are many ways to show division by 2,
this machine is a bit lazy and will always opt for the easiest function.

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Function Machine Division: If you think the numbers are being divided by 2, simply enter ÷2.While there are many ways to show division by 2,this machine is a bit lazy and will always opt for the easiest function.

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By Vitor

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http://www.shodor.org/interactivate/activities/LinearFunctMachine/
- Henrique

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A function is a rule that connects two sets

It has 3 parts
The input
The relationship
The output

f(x) is the way to express a funtio
By Julian

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http://www.shodor.org/interactivate/activities/LinearFunctMachine/

By Julian

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The mathematical concept of a function emerged in the 17th century.
Mathematicians of the 18th century typically regarded a function as being defined by an analytic expression. Functions in the 19th century was used in geometry too
By Julian

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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.

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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.

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-Vitor

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The evolution of the concept of function goes back 4000 years; 3,700 of these consist of anticipations. The idea evolved for close to 300 years in intimate connection with problems in calculus and analysis. In fact, a one-sentence definition of analysis as the study of properties of various classes of functions would not be far off the mark. Moreover, the concept of function is one of the distinguishing features of “modern” as against “classical” mathematics.
----Christina

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https://www.youtube.com/watch?v=kvGsIo1TmsM
- Polly

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A function is a rule which relates the values of one variable quantity to the values of another variable quantity.
Example:
f(x)
- Polly

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Special activity or purpose of a person or thing

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https://www.khanacademy.org/math/algebra/algebra-functions/evaluating-functions/v/what-is-a-function

----Christina

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In mathematics, a function[1] 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 x ². 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"[2] 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.

In modern mathematics,[3] 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 (or target); and the set of all input-output pairs, called its graph. Sometimes the codomain is called the function's "range", but more commonly the word "range" is used to mean, instead, specifically the set of outputs (this is also called the image of the function). For example, we could define a function using the rule f(x) = x ² by saying that the domain and codomain are the real numbers, and that the graph consists of all pairs of real numbers (x, x ²). The image of this function is the set of non-negative real numbers. 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.

- By Toby

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http://www.mathplayground.com/functionmachine.html

-chae

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- Toby

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It must work for every possible input value

And it has only one relationship for each input value

- Henrique

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Formal Definition of Function by Henrique

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Formal Definition of Function by Henrique

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A function relates each element of a set
with exactly one element of another set
(possibly the same set).

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f(x)=ax+b
-Daniel

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Math definition--An expression that involving one or more variables.

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function is a relationship which each input has single output.
F(x)
x

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A function is like a machine that has an input and an output.
- Henrique (The Best)
I like that you changed the color.-Mr. Rico

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Functions before the 17th century. According to Dieudonné and Ponte, the concept of a function emerged in the 17th century as a result of the development of analytic geometry and the infinitesimal calculus. Nevertheless, Medvedev suggests that the implicit concept of a function is one with an ancient lineage.

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Functions before the 17th century. According to Dieudonné and Ponte, the concept of a function emerged in the 17th century as a result of the development of analytic geometry and the infinitesimal calculus. Nevertheless, Medvedev suggests that the implicit concept of a function is one with an ancient lineage.

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- Ary

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Ary

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 Definition : Function is a relation or expression involving one or more variables."the function (bx + c)"

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 Definition : Function is a relation or expression involving one or more variables."the function (bx + c)"

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- Ary

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https://en.wikipedia.org/wiki/Function_(mathematics)
- Robin

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https://en.wikipedia.org/wiki/Function_(mathematics)

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More in

https://www.google.com.hk/search?q=Function+games&safe=strict&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjBwbeWpIjXAhWBEbwKHSRVCgoQ_AUICigB&biw=1366&bih=662#imgrc=PzDQE8db4kXLPM:
-Robin

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http://www.mathplayground.com/functionmachine.html
-Robin

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https://www.youtube.com/watch?v=kvGsIo1TmsM
-Robin

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f(x)=x 2
F is the function name
X is the input
x 2 is what to output
- Connor

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http://www.mathplayground.com/functionmachine.html
-Robin

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x 2
x ³+1
Many more
- Connor

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Classic way of writing a function
- Connor

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The input
The relationship
The output
- Connor

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A function relates an input to an output.
- Connor

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Please choose at least 3 tasks and post it here. You need to do some research about function.
Task:
1. Find a brief History of Functions
2. Find the definition and examples of functions
3. Find an online game that uses Function Machine
4. Find a function game (not online).
5. Find a video about Function.