What is Function (mathematics)?
In [[mathematics]], a '''function''' is a mathematical [[object]] that produces an [[output]], when given an [[input]] (which could be a [[number]], a [[vector]], or anything that can exist inside a [[set]] of things). [[File:FunctionProcess.png|right|300px]] In essence, a function is like a machine, that takes a value of <math>x</math> and returns an output <math>y</math>. The set of all values that <math>x</math> can have is called the ''domain'', and the set that contains every value that <math>y</math> can have is called the ''codomain''. A function is often denoted by italic letters such as <math>f</math>, <math>g</math>, <math>h</math>.<ref>{{Cite web|date=2020-03-01|title=Compendium of Mathematical Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/|access-date=2020-08-17|website=Math Vault|language=en-US}}</ref><ref>{{Cite web|title=What is a Function|url=http://www.mathisfun.com/sets/function|access-date=2020-08-17|website=www.mathisfun.com|language=en-US}}</ref><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Function|url=https://mathworld.wolfram.com/Function.html|access-date=2020-08-17|website=mathworld.wolfram.com|language=en}}</ref> If this happens, then we say that <math>y</math> is a function of <math>x</math>, and we write <math>y=f(x)</math>. Here, <math>f</math> is the name of the function, and one writes <math>f:X	o Y</math> (function from X to Y) to represent the three parts of the function: the domain (<math>X</math>), the [[codomain]] (<math>Y</math>), and the pairing process (the arrow), or, the mapping from and to the sets. An example of a function is <math>f(x)=x+1</math>. One gives a [[natural number]] <math>x</math> as the input, and gets a [[natural number]] <math>y</math>, which is <math>x+1</math>. For example, giving 3 as input to <math>f</math> results in an output of 4. A function doesn't have to be an [[equation]]. The main idea is that inputs and outputs are paired up somehow—even if the process might be very complicated. == Metaphors == === Tables === [[Fil