function

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The action or purpose for which a person or thing is suited or employed, especially.
• noun A person's role or occupation.
• noun Biology The physiological activity of an organ or body part.
• noun Computers A procedure within an application.
• noun An official ceremony or a formal social occasion.
• noun Something closely related to another thing and dependent on it for its existence, value, or significance.
• noun A variable so related to another that for each value assumed by one there is a value determined for the other.
• noun A rule of correspondence between two sets such that there is exactly one element in the second set assigned to each element in the first set.
• intransitive verb To have or perform a function; serve.
• intransitive verb To deal with or overcome the challenges of everyday life.

from The Century Dictionary.

• To perform a function; work; act; functionate; especially, in physiology, to have a function; do or be something physiologically.
• noun Fulfilment or discharge of a set duty or requirement; exercise of a faculty or office.
• noun Activity in general; action of any kind; behavior.
• noun Power of acting; faculty; that power of acting in a specific way which appertains to a thing by virtue of its special constitution; that mode of action or operation which is proper to any organ, faculty, office, structure, etc.
• noun That which one is bound or which is one's business to do; business; office; duty; employment.
• noun An official ceremony.
• noun Any important occasion marked by elaborate ceremonial: extended in recent use to cover social entertainments, as operas, balls, and receptions.
• noun In mathematics, a mathematical quantity whose value depends upon the values of other quantities, called the arguments or independent variables of the function; a mathematical quantity whose changes of value depend on those of other quantities called its variables.
• noun Hence, anything which is dependent for its value, significance, etc., upon something else.
• noun See the adjectives.
• noun see the adjectives.
• noun See the adjectives.
• noun One of several functions related to in the same manner in which ordinary elliptic functions are related to , being merely transformed elliptic functions.
• noun See the adjectives.
• noun a function such that the interval of the variable considered may be so divided into parts that the function is continuous, differentiable, etc., in each part.
• noun In a generalized sense, a function which has its value unchanged by the substitution for its variable of a certain algebraic function thereof. A periodic function of the second kind is one for which this function is linear.
• noun Two physical quantities whose several mathematical relations to two other physical quantities are the same.
• noun which may, for instance, be either limited or unlimited.
• noun See graph.
• noun A function differing from that just defined by log/r.

from the GNU version of the Collaborative International Dictionary of English.

• intransitive verb To execute or perform a function; to transact one's regular or appointed business.
• noun The act of executing or performing any duty, office, or calling; performance.
• noun (Physiol.) The appropriate action of any special organ or part of an animal or vegetable organism
• noun The natural or assigned action of any power or faculty, as of the soul, or of the intellect; the exertion of an energy of some determinate kind.
• noun The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession.
• noun (Math.) A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
• noun (Eccl.) A religious ceremony, esp. one particularly impressive and elaborate.
• noun A public or social ceremony or gathering; a festivity or entertainment, esp. one somewhat formal.
• noun a quantity whose connection with the variable is expressed by an equation that involves only the algebraic operations of addition, subtraction, multiplication, division, raising to a given power, and extracting a given root; -- opposed to transcendental function.
• noun See under Arbitrary.
• noun See under Calculus.
• noun (Thermo-dynamics) a relation between the amount of heat given off by a source of heat, and the work which can be done by it. It is approximately equal to the mechanical equivalent of the thermal unit divided by the number expressing the temperature in degrees of the air thermometer, reckoned from its zero of expansion.
• noun See Inverse trigonometrical functions (below). -- Continuous function, a quantity that has no interruption in the continuity of its real values, as the variable changes between any specified limits.
• noun See under Discontinuous.
• noun a large and important class of functions, so called because one of the forms expresses the relation of the arc of an ellipse to the straight lines connected therewith.
• noun a quantity directly expressed in terms of the independently varying quantity; thus, in the equations y = 6x2, y = 10 -x3, the quantity y is an explicit function of x.
• noun a quantity whose relation to the variable is expressed indirectly by an equation; thus, y in the equation x2 + y2 = 100 is an implicit function of x.
• noun the lengths of arcs relative to the sines, tangents, etc. Thus, AB is the arc whose sine is BD, and (if the length of BD is x) is written sin -1x, and so of the other lines. See Trigonometrical function (below). Other transcendental functions are the exponential functions, the elliptic functions, the gamma functions, the theta functions, etc.