Functions

From The Collaborative International Dictionary of English v.0.48 [gcide]:

1. A current of water; a stream. [Obs.]

2. [Cf. F. fluente.] (Math.) A variable quantity, considered as increasing or diminishing; -- called, in the modern calculus, the {function} or {integral}.

From The Collaborative International Dictionary of English v.0.48 [gcide]:

Function \Func"tion\, noun [L. functio, fr. fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. {Defunct}.]

1. The act of executing or performing any duty, office, or calling; performance. "In the function of his public calling." --Swift.

2. (Physiol.) The appropriate action of any special organ or
part of an animal or vegetable organism; as, the function
of the heart or the limbs; the function of leaves, sap,
roots, etc.; life is the sum of the **functions** of the
various organs and parts of the body.

3. 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.

As the mind opens, and its **functions** spread. --Pope.

4. The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession.

Tradesmen . . . going about their **functions**. --Shak.

The malady which made him incapable of performing
his
regal **functions**. --Macaulay.

5. (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 x^{2}, 3^{x}, Log. x, and
Sin. x, are all **functions** of x.

6. (Eccl.) A religious ceremony, esp. one particularly impressive and elaborate.

Every solemn 'function' performed with the requirements of the liturgy. --Card. Wiseman. [Webster 1913 Suppl.]

7. A public or social ceremony or gathering; a festivity or entertainment, esp. one somewhat formal.

This function, which is our chief social event. --W. D. Howells. [Webster 1913 Suppl.]

{Algebraic function}, 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.

{Arbitrary function}. See under {Arbitrary}.

{Calculus of **functions**}. See under {Calculus}.

{Carnot's function} (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.

{Circular **functions**}. 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.

{Discontinuous function}. See under {Discontinuous}.

{Elliptic **functions**}, 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.

{Explicit function}, a quantity directly expressed in terms of the independently varying quantity; thus, in the equations y = 6x^{2}, y = 10 -x^{3}, the quantity y is an explicit function of x.

{Implicit function}, a quantity whose relation to the variable is expressed indirectly by an equation; thus, y in the equation x^{2} + y^{2} = 100 is an implicit function of x.

{Inverse trigonometrical **functions**}, or {Circular **functions**},
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 ^{-1}x, 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.

{One-valued function}, a quantity that has one, and only one,
value for each value of the variable. -- {Transcendental
**functions**}, a quantity whose connection with the variable
cannot be expressed by algebraic operations; thus, y in
the equation y = 10^{x} is a transcendental function of x.
See {Algebraic function} (above). -- {Trigonometrical
function}, a quantity whose relation to the variable is the
same as that of a certain straight line drawn in a circle
whose radius is unity, to the length of a corresponding
are of the circle. Let AB be an arc in a circle, whose
radius OA is unity let AC be a quadrant, and let OC, DB,
and AF be drawnpependicular to OA, and EB and CG parallel
to OA, and let OB be produced to G and F. E Then BD is the
sine of the arc AB; OD or EB is the cosine, AF is the
tangent, CG is the cotangent, OF is the secant OG is the
cosecant, AD is the versed sine, and CE is the coversed
sine of the are AB. If the length of AB be represented by
x (OA being unity) then the lengths of **Functions**. these
lines (OA being unity) are the trigonometrical **functions**
of x, and are written sin x, cos x, tan x (or tang x), cot
x, sec x, cosec x, versin x, coversin x. These quantities
are also considered as **functions** of the angle BOA.
Function

From The Collaborative International Dictionary of English v.0.48 [gcide]:

Function \Func"tion\ (f[u^][ng]k"sh[u^]n), Functionate \Func"tion*ate\, verb (used without an object) To execute or perform a function; to transact one's regular or appointed business.

From WordNet (r) 3.0 (2006) [wn]:

noun

1: (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) [syn: {function}, {mathematical function}, {single-valued function}, {map}, {mapping}]

2: what something is used for; "the function of an auger is to bore holes"; "ballet is beautiful but what use is it?" [syn: {function}, {purpose}, {role}, {use}]

3: the actions and activities assigned to or required or expected of a person or group; "the function of a teacher"; "the government must do its part"; "play its role" [syn: {function}, {office}, {part}, {role}]

4: a relation such that one thing is dependent on another; "height is a function of age"; "price is a function of supply and demand"

5: a formal or official social gathering or ceremony; "it was a black-tie function"

6: a vaguely specified social event; "the party was quite an
affair"; "an occasion arranged to honor the president"; "a
seemingly endless round of social **functions**" [syn: {affair},
{occasion}, {social occasion}, {function}, {social function}]

7: a set sequence of steps, part of larger computer program [syn: {routine}, {subroutine}, {subprogram}, {procedure}, {function}]

verb

1: perform as expected when applied; "The washing machine won't go unless it's plugged in"; "Does this old car still run well?"; "This old radio doesn't work anymore" [syn: {function}, {work}, {operate}, {go}, {run}] [ant: {malfunction}, {misfunction}]

2: serve a purpose, role, or function; "The tree stump serves as
a table"; "The female students served as a control group";
"This table would serve very well"; "His freedom served him
well"; "The table **functions** as a desk" [syn: {serve},
{function}]

3: perform duties attached to a particular office or place or function; "His wife officiated as his private secretary" [syn: {officiate}, {function}]

The dictionary definitions are retrieved from a local copy of two of the open source __ DICT__ dictionaries. Click

Friday, March 27, 2015 8:52:57 PM Coordinated Universal Time (UTC)

DEFINE.COM_Functions_2015-03-27_20-52-57_54-161-234-150