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function (n.)

1530s, "one's proper work or purpose; power of acting in a specific proper way," from French fonction (16c.) and directly from Latin functionem (nominative functio) "a performance, an execution," noun of action from funct-, past-participle stem of fungi "perform, execute, discharge," from PIE *bhung- "be of use, be used" (source also of Sanskrit bhunjate "to benefit, make benefit, atone," Armenian bowcanem "to feed," Old Irish bongaid "to break, harvest"), which is perhaps related to root *bhrug- "to enjoy." Meaning "official ceremony" is from 1630s, originally in church use. Use in mathematics probably was begun by Leibnitz (1692). In reference to computer operations, 1947.

function (v.)

1844, "perform a function" (intransitive), from function (n.). Related: Functioned; functioning.

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Definitions of function
1
function (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: mathematical function / single-valued function / map / mapping
function (n.)
what something is used for;
the function of an auger is to bore holes
Synonyms: purpose / role / use
function (n.)
the actions and activities assigned to or required or expected of a person or group;
the function of a teacher
Synonyms: office / part / role
function (n.)
a relation such that one thing is dependent on another;
price is a function of supply and demand
height is a function of age
function (n.)
a formal or official social gathering or ceremony;
it was a black-tie function
function (n.)
a vaguely specified social event;
a seemingly endless round of social functions
Synonyms: affair / occasion / social occasion / social function
function (n.)
a set sequence of steps, part of larger computer program;
Synonyms: routine / subroutine / subprogram / procedure
2
function (v.)
perform as expected when applied;
Synonyms: work / operate / go / run
function (v.)
serve a purpose, role, or function;
The table functions as a desk
Synonyms: serve
function (v.)
perform duties attached to a particular office or place or function;
Synonyms: officiate
From wordnet.princeton.edu