The image of a function is the collection of values from the co-domain that are actually achieved.

$Im(f)~=~\{~y:~\exists~x\in{D}~s.t.~f(x)=y~\}$

where $D$ is the domain of the function.

See also:

BirthdayProblem Calculus ChainRule CommutativeOperation CubeRoot DifferentialCalculus DomainOfAFunction EquationOfALine EulersNumber Factorial HolomorphicFunction HyperbolicFunction IntegralCalculus IntegrationByParts LinearFunction Logarithm MathematicsTaxonomy NewtonsMethod OrdinaryDifferentialEquation PartialDifferentialEquation RiemannHypothesis RiemannZetaFunction TrigonometricFunction	AGentleIntroductionToTimeComplexity InverseFunction RiemannSurface			AbsoluteValue AlgebraicNumber EuclideanAlgorithm FactoringQuadratics ImaginaryNumber IrrationalNumber MagnitudeOfAVector Root RootTwoIsIrrational Surd
↓	↓		↓	↓
Function			CoDomainOfAFunction RangeOfAFunction SquareRoot
			↓
		⇌	You are here ImageOfAFunction
			↓
			DomainOfAFunction
↓	↓		↓	↓
CoDomainOfAFunction Polynomial RangeOfAFunction	RealNumber			AlgebraicNumber ComplexNumber Integer RationalNumber

Local neighbourhood - D3

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Image Of A Function