Etymology
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Words related to function

*bhrug- 
*bhrūg-, Proto-Indo-European root meaning "to enjoy," with derivatives referring to agricultural products.

It forms all or part of: brook (v.) "to endure;" defunct; fructify; fructose; frugal; fruit; fruitcake; fruitful; fruition; fruitless; frumentaceous; function; fungible; perfunctory; tutti-frutti; usufruct.

It is the hypothetical source of/evidence for its existence is provided by: Latin frui "to use, enjoy," fructus "an enjoyment, proceeds, fruit, crops;" Old English brucan "use, enjoy, possess," German brauchen "to use."
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defunct (adj.)

"dead, deceased, extinct," 1590s, from Old French defunct (14c., Modern French defunt) or directly from Latin defunctus "dead," literally "off-duty," past-participle adjective from defungi "to discharge, finish," from de- "off, completely" (see de-) + fungi "perform or discharge duty" (see function (n.)).

dysfunction (n.)

"failure to function, abnormality or impairment of function," 1914, from dys- "bad, abnormal, difficult" + function (n.). Originally in anatomy and medicine; in sociology by 1949.

functional (adj.)
1630s, "pertaining to function or office," from function (n.) + -al (1), or from Medieval Latin functionalis. Meaning "utilitarian" is by 1864; specific use in architecture is from 1928. Related: Functionally; functionality.
functionary (n.)
"one who has a certain function, one who holds an office," 1791, from or patterned on French fonctionnaire, a word of the Revolution; from fonction (see function (n.)). As an adjective in English from 1822, "functional." Related: Functionarism.
fungible (adj.)
"capable of being used in place of another; capable of being replaced," 1818, a word in law originally, from Medieval Latin fungibilis, from Latin fungi "perform" (see function (n.)) via phrases such as fungi vice "to take the place." Earlier as a noun (1765).
malfunction (n.)

"a faulty functioning, a failure to function as expected," 1827, from mal- "bad, badly, wrong" + function. As a verb, "to fail to function normally or as expected," by 1888. Related: Malfunctioned; malfunctioning.

perfunctory (adj.)

"done mechanically or without interest or zeal and merely for the sake of being rid of the duty of doing it; done so as to conform to the letter but not the spirit," 1580s, from Late Latin perfunctorius "careless, negligent," literally "like one who wishes to get through a thing," from Latin perfungus, past participle of perfungi "discharge, busy oneself, get through," from per "through" (from PIE root *per- (1) "forward," hence "through") + fungi "perform" (see function (n.)). Related: Perfunctorily.