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noun
1.
the kind of action or activity proper to a person, thing, or institution; the purpose for which something is designed or exists; role.
2.
any ceremonious public or social gathering or occasion.
3.
a factor related to or dependent upon other factors:
Price is a function of supply and demand.
4.
Mathematics.

Also called correspondence, map, mapping, transformation. a relation between two sets in which one element of the second set is assigned to each element of the first set, as the expression y = x 2 ; operator.
Also called multiple-value function. a relation between two sets in which two or more elements of the second set are assigned to each element of the first set, as y 2 = x 2 , which assigns to every x the two values y = + x and y = − x.
a set of ordered pairs in which none of the first elements of the pairs appears twice.

5.
Geometry.

a formula expressing a relation between the angles of a triangle and its sides, as sine or cosine.
hyperbolic function.

6.
Grammar.

the grammatical role a linguistic form has or the position it occupies in a particular construction.
the grammatical roles or the positions of a linguistic form or form class collectively.

7.
Sociology. the contribution made by a sociocultural phenomenon to an ongoing social system.
verb (used without object)
8.
to perform a specified action or activity; work; operate:
The computer isn’t functioning now. He rarely functions before noon.
9.
to have or exercise a function; serve:
In earlier English the present tense often functioned as a future. This orange crate can function as a chair.
noun
1.
the natural action or intended purpose of a person or thing in a specific role: the function of a hammer is to hit nails into wood
2.
an official or formal social gathering or ceremony
3.
a factor dependent upon another or other factors: the length of the flight is a function of the weather
4.
(maths, logic) Also called map, mapping. a relation between two sets that associates a unique element (the value) of the second (the range) with each element (the argument) of the first (the domain): a many-one relation. Symbol: f(x) The value of f(x) for x = 2 is f(2)
verb (intransitive)
5.
to operate or perform as specified; work properly
6.
(foll by as) to perform the action or role (of something or someone else): a coin may function as a screwdriver

function func·tion (fŭngk’shən)
n.

The physiological property or the special action of an organ or a body part.

Something closely related to another thing and dependent on it for its existence, value, or significance, such as growth resulting from nutrition.

A mathematical variable so related to another that for each value assumed by one there is a value determined for the other.

A rule of correspondence between two sets such that there is a unique element in the second set assigned to each element in the first set.

The general properties of a substance, depending on its chemical character and relation to other substances, that provide the basis upon which it may be grouped as among acids or bases.

A particular reactive grouping in a molecule.

function
(fŭngk’shən)

A relationship between two sets that matches each member of the first set with a unique member of the second set. Functions are often expressed as an equation, such as y = x + 5, meaning that y is a function of x such that for any value of x, the value of y will be 5 greater than x.

A quantity whose value depends on the value given to one or more related quantities. For example, the area of a square is a function of the length of its sides.

function definition

In mathematics, a quantity whose value is determined by the value of some other quantity. For example, “The yield of this field is a function of the amount of fertilizer applied” means that a given amount of fertilizer will yield an amount of whatever crop is growing.