ETYM Latin functio, from fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. French fonction. Related to Defunct.
1. What something is used for; SYN. purpose, role, use.
2. A relation such that one thing is dependent on another.
3. The actions and activities assigned to or required or expected of a person or group; SYN. office, part, role.
4. A mathematical relation such that each element of one set is associated with at least one element of another set; SYN. mathematical function.
5. A formal or official social gathering or ceremony.

In mathematics, a function f is a non-empty set of ordered pairs (x,f(x)) of which no two can have the same first element. Hence, if f(x) = x2 two ordered pairs are (-2,4) and (2,4). The set of all first elements in a function’s ordered pairs is called the domain; the set of all second elements is the range. In the algebraic expression y = 4x3 + 2, the dependent variable y is a function of the independent variable x, generally written as f(x). Functions are used in all branches of mathematics, physics, and science generally; for example, the formula t = 2pÖ(l/g) shows that for a simple pendulum the time of swing t is a function of its length l and of no other variable quantity (p and g, the acceleration due to gravity, are constants).

To work or operate properly; SYN. work, operate, go, run.