A "Function" takes elements from one collection (domain of a function) and assigns to it, or returns, an element from another collection (co-domain of a function, image of a function, range of a function).

Functions appear everywhere in mathematics. Examples include:

Simple polynomials: $f(x)~=~x^3-2x+5$
Exponential functions: $f(x)~=~e^x$

However, functions can be much more complex, not described by a single formula, and functions don't necessarily work only and/or entirely on the real numbers. Functions in general carry elements of one set to another set, not necessarily the same.

(none)	(none)			AGentleIntroductionToNPC AbsoluteValue AlgebraicNumber BasinOfAttraction Commutative DifferentiatingPolynomials DifferentiatingTrigFunctions EuclideanAlgorithm Euler FactoringQuadratics HyperbolicCosine HyperbolicSin ImaginaryNumber IrrationalNumber IsaacNewton LinearAlgebra MagnitudeOfAVector ModellingEpidemics NamingPhilosophy NaturalLogarithm NewtonRaphsonMethod NonEuclideanGeometry PascalsTriangle Permutation PrimeNumberTheorem ProductRule QuotientRule Root RootTwoIsIrrational SimpleHarmonicMotion SuggestedReading Surd TimeComplexity UnitCircle ZeroFactorial
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CoDomainOfAFunction DomainOfAFunction ImageOfAFunction RangeOfAFunction			AGentleIntroductionToTimeComplexity BirthdayProblem Calculus ChainRule CommutativeOperation CubeRoot DifferentialCalculus EquationOfALine EulersNumber Factorial HolomorphicFunction HyperbolicFunction IntegralCalculus IntegrationByParts InverseFunction LinearFunction Logarithm MathematicsTaxonomy NewtonsMethod OrdinaryDifferentialEquation PartialDifferentialEquation RiemannHypothesis RiemannSurface RiemannZetaFunction SquareRoot TrigonometricFunction
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		⇌	You are here Function
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			Polynomial RealNumber
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Integer	AlgebraicNumber ComplexNumber RationalNumber			CauchySequence ContinuedFraction DedekindCut FundamentalTheoremOfAlgebra IrrationalNumber RootsOfPolynomials TranscendentalNumber

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