In the old "Schoolhouse Rock" song, "Conjunction junction, what's your function?," the word function means, "What does a conjunction do?" The famous design dictum "form follows function" tells us that an object's design should reflect what it does.
Function is one of those words that gets used a lot and means lots of different things. It means what something does, but also what a person does, whether something or someone is doing what they should, and crazily enough, a big party. "Your function is to bring the senator coffee at the political function. He cannot function without it."
Primary Meanings of function
1. 
nv 
what something is used for
serve a purpose, role, or function

2. 
n 
a relation such that one thing is dependent on another

3. 
n 
a formal or official social gathering or ceremony

4. 
n 
a set sequence of steps, part of larger computer program

Full Definitions of function
1
n what something is used for
“the
function of an auger is to bore holes”
 Types:

raison d'etre
the purpose that justifies a thing's existence
 Type of:

usefulness, utility
the quality of being of practical use
n the actions and activities assigned to or required or expected of a person or group
“the
function of a teacher”
 Types:
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capacity
a specified function

hat
an informal term for a person's role

portfolio
the role of the head of a government department

lieu, place, position, stead
the post or function properly or customarily occupied or served by another

second fiddle
a secondary role or function

behalf
as the agent of or on someone's part (usually expressed as "on behalf of" rather than "in behalf of")
 Type of:

duty
work that you are obliged to perform for moral or legal reasons
v serve a purpose, role, or function
v perform as expected when applied
 Antonyms:

malfunction, misfunction
fail to function or function improperly
 Types:
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double
do double duty; serve two purposes or have two functions

roll
begin operating or running

run
be operating, running or functioning

cut
function as a cutting instrument

serve, service
be used by; as of a utility
2
n a relation such that one thing is dependent on another
“height is a
function of age”
“price is a
function of supply and demand”
 Type of:

relation
an abstraction belonging to or characteristic of two entities or parts together
n (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
 Synonyms:
 map, mapping, mathematical function, singlevalued function
 Types:
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multinomial, polynomial
a mathematical function that is the sum of a number of terms

expansion
a function expressed as a sum or product of terms

inverse function
a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x

Kronecker delta
a function of two variables i and j that equals 1 when i=j and equals 0 otherwise

metric, metric function
a function of a topological space that gives, for any two points in the space, a value equal to the distance between them

transformation
(mathematics) a function that changes the position or direction of the axes of a coordinate system

isometry
a onetoone mapping of one metric space into another metric space that preserves the distances between each pair of points

operator
(mathematics) a symbol or function representing a mathematical operation

circular function, trigonometric function
function of an angle expressed as a ratio of the length of the sides of rightangled triangle containing the angle

threshold function
a function that takes the value 1 if a specified function of the arguments exceeds a given threshold and 0 otherwise

exponential, exponential function
a function in which an independent variable appears as an exponent

biquadratic, biquadratic polynomial, quartic polynomial
a polynomial of the fourth degree

homogeneous polynomial
a polynomial consisting of terms all of the same degree

monic polynomial
a polynomial in one variable

quadratic, quadratic polynomial
a polynomial of the second degree

series
(mathematics) the sum of a finite or infinite sequence of expressions

reflection
(mathematics) a transformation in which the direction of one axis is reversed

rotation
(mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin

translation
(mathematics) a transformation in which the origin of the coordinate system is moved to another position but the direction of each axis remains the same

affine transformation
(mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axis

linear operator
an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)

identity, identity element, identity operator
an operator that leaves unchanged the element on which it operates

sin, sine
ratio of the length of the side opposite the given angle to the length of the hypotenuse of a rightangled triangle

arc sine, arcsin, arcsine, inverse sine
the inverse function of the sine; the angle that has a sine equal to a given number

cos, cosine
ratio of the adjacent side to the hypotenuse of a rightangled triangle

arc cosine, arccos, arccosine, inverse cosine
the inverse function of the cosine; the angle that has a cosine equal to a given number

tan, tangent
ratio of the opposite to the adjacent side of a rightangled triangle

arc tangent, arctan, arctangent, inverse tangent
the inverse function of the tangent; the angle that has a tangent equal to a given number

cotan, cotangent
ratio of the adjacent to the opposite side of a rightangled triangle

arc cotangent, arccotangent, inverse cotangent
the inverse function of the cotangent; the angle that has a cotangent equal to a given number

sec, secant
ratio of the hypotenuse to the adjacent side of a rightangled triangle

arc secant, arcsec, arcsecant, inverse secant
the inverse function of the secant; the angle that has a secant equal to a given number

cosec, cosecant
ratio of the hypotenuse to the opposite side of a rightangled triangle

arc cosecant, arccosecant, inverse cosecant
the angle that has a cosecant equal to a given number
 Type of:

mathematical relation
a relation between mathematical expressions (such as equality or inequality)
3
n a formal or official social gathering or ceremony
“it was a blacktie
function”
 Type of:

social affair, social gathering
a gathering for the purpose of promoting fellowship
n a vaguely specified social event
“a seemingly endless round of social
functions”
 Synonyms:
 affair, occasion, social function, social occasion
 Types:
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party
an occasion on which people can assemble for social interaction and entertainment

celebration, jubilation
a joyful occasion for special festivities to mark some happy event

ceremonial, ceremonial occasion, ceremony, observance
a formal event performed on a special occasion

fundraiser
a social function that is held for the purpose of raising money

photo op, photo opportunity
an occasion that lends itself to (or is deliberately arranged for) taking photographs that provide favorable publicity for those who are photographed

sleepover
an occasion of spending a night away from home or having a guest spend the night in your home (especially as a party for children)

bash, brawl, do
an uproarious party

birthday party
a party held on the anniversary of someone's birth

bunfight, bunfight
(Briticism) a grand formal party on an important occasion

ceilidh
an informal social gathering at which there is Scottish or Irish folk music and singing and folk dancing and story telling

cocktail party
an afternoon party at which cocktails are served

dance
a party for social dancing

feast, fete, fiesta
an elaborate party (often outdoors)

house party
a party lasting over one or more nights at a large house

jolly
a happy party

tea party
a party at which tea is served

whist drive
a progressive whist party

circumstance
formal ceremony about important occasions

funeral
a ceremony at which a dead person is buried or cremated

hymeneals, nuptials, wedding, wedding ceremony
the social event at which the ceremony of marriage is performed

pageant, pageantry
a rich and spectacular ceremony

dedication
a ceremony in which something (as a building) is dedicated to some goal or purpose

opening
a ceremony accompanying the start of some enterprise

commemoration, memorialisation, memorialization
a ceremony to honor the memory of someone or something

military ceremony
a formal ceremony performed by military personnel

induction, initiation, installation
a formal entry into an organization or position or office

exercise
(usually plural) a ceremony that involves processions and speeches

fire walking
the ceremony of walking barefoot over hot stones or a bed of embers

formalities, formality
a requirement of etiquette or custom

Maundy
a public ceremony on Maundy Thursday when the monarch distributes Maundy money

potlatch
a ceremonial feast held by some Indians of the northwestern coast of North America (as in celebrating a marriage or a new accession) in which the host gives gifts to tribesmen and others to display his superior wealth (sometimes, formerly, to his own impoverishment)
 Type of:

social event
an event characteristic of persons forming groups
4
n a set sequence of steps, part of larger computer program
 Synonyms:
 procedure, routine, subprogram, subroutine
 Types:
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cataloged procedure
a set of control statements that have been placed in a library and can be retrieved by name

contingency procedure
an alternative to the normal procedure; triggered if an unusual but anticipated situation arises

library routine
a debugged routine that is maintained in a program library

random number generator
a routine designed to yield a random number

recursive routine
a routine that can call itself

reusable routine
a routine that can be loaded once and executed repeatedly

executive routine, supervisory routine
a routine that coordinates the operation of subroutines

tracing routine
a routine that provides a chronological record of the execution of a computer program

service routine, utility routine
a routine that can be used as needed

dump routine
a routine that writes from an internal store to some external medium

input routine
a routine that writes from an external source to an internal store

output routine
a routine that controls an output device
 Type of:

computer software, package, software, software package, software program, software system
(computer science) written programs or procedures or rules and associated documentation pertaining to the operation of a computer system and that are stored in read/write memory