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

- Henrique

 

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) = 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). 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

              ----Christina

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.
by Vitor