Download Functions 1 2.2 Definition of a Function

Mathematical Investigations II
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Mathematical Investigations II
Definitions of Function
A function is
Your MI-2 Class
A function is a correspondence between two sets that associates with each element of the first set
a unique element of the second set. The first set is called the domain of the function. For each
element x of the domain, the corresponding element y of the second set is called the image
of x under the function. The set of all images of the elements of the domain is called the range
of the function.
p. 244, Algebra and Trigonometry by Johnson, et al., 1967
A function is a relation with the property: If (a,b) and (a,c) belong to the relation, then b = c.
The set of all first entries of the ordered pairs is called the domain of the function, and the set of
all second entries is called the range of the function.
p. 18, College Algebra, A Graphing Approach by Demana & Waits, 1990
A function is a correspondence between two variables such that each value of the first variable
corresponds to exactly one value of the second variable.
p. 375, Advanced Algebra by UCSMP, 1990
A function is a relation in which, for each ordered pair, the first coordinate has exactly one
second coordinate.
p. 378, Advanced Algebra by UCSMP, 1990
The domain of a function is the set of values that are allowable substitutions for the independent
variable. The range of a function is the set of values that can result from the substitutions for
the independent variable.
p. 382, Advanced Algebra by UCSMP, 1990
A function is a relationship between two variables such that to each value of the independent
variable there corresponds exactly one value of the dependent variable.
The collection of all values assumed by the independent variable is called the domain of the
function, and the collection of all values assumed by the dependent variable is called the range
of the function.
p. 137, Algebra and Trigonometry by Larson & Hostetler, 1985
Funct. 2.1
RevF07
Mathematical Investigations II
Name:
A function is a relation that pairs each input with exactly one output.
The domain of a function is the set of all inputs for which the function produces a meaningful
output. The range of a function is the set of all the function's meaningful outputs.
p. 184, Algebra 2 and Trigonometry, Benson, et al., 1991
A function is a correspondence or rule that assigns to every element in a set D exactly one
element in a set R. The set D is called the domain of the function, and the set R is called the
range.
p. 119, Advanced Mathematics, Precalculus with
Discrete Mathematics and Data Analysis
Richard G. Brown, 1994
Any set of ordered pairs is called a relation. A function is a relation that assigns exactly one
value of the dependent variable to each value of the independent variable.
p. 73, Prentice Hall Algebra, 1998
O functie f definita pe A si cu valori în B este un triplet (A, B, f) unde A si B sînt multimi nevide
iar f este o regula care atribuie fiecarui element din A exact un element în B.
Romanian
Une fonction f d'A à B, c'est un triplet (A,B,f) où A et B sont les ensembles non-vides et f est
une règle qui assigne à chaque élément en A exactement un élément en B.
French
Eine Funktion Namen F von A bis B ist eine Dreierzruppe (A, B, f), vorin A und B heine
Nullsätze sind, und f ist ein regel, das jeder Element in A mit genau einem Element in B
zusammenpasst.
German
При зтом x называют независимой переменной или аргументом, а y -- зависимой
переменной или функцией.
Russian
Una función es un tipo de relación en que cada elemento del dominio se parea exactamente con
un elemento de la amplitudo.
Spanish
Um função é uma relação entre dois conjuntos que a cada elemento do primeiro conjunto
faz corresponder um e só um elemento do segundo.
Portuguese
Funct. 2.2
RevF07