Fūnction, n.

(fŭŋk'shun), n. [Lat. functio, from fungi, functus, to perform, execute; Fr. fonction, Sp. funcion, It. funzione.] 1. The act of executing, or performing activity, duty, office, or calling; performance. That function is swallowed in surmise. Shak. A representing commoner in the function of his public calling. Swift. 2. The peculiar or appointed action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the natural or assigned action of any power or faculty of the soul, or of the intellect; the exertion of an energy of some determinate kind. As the mind opens, and its functions spread. Pope. 3. The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession. Tradesmen singing in their shops, and going about their functions friendly. Shak. Every soldier was able to do all the functions of an officer. Burnet. 4. (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. The dependent 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:—usually indicated by the symbol f, F, or φ; as, y = F(x), denoting that y is the function of x, or is dependent for its value on x.