One occupation is a rule that relates each element of a set A to a single element of the set B. In this definition, set A is called domain, and set B is the counter-domain of the function. In addition to these two sets, there is a subset of counter-domain called Image.
The representation of a function in algebraic form can be done as follows:
Data the sets A and B, a occupation f is the rule:
f: A → B
y = f(x)
the symbology THE → B means that the elements of set A are related to the elements of set B through the occupation f. In other words, given any element belonging to the set A, this element will be related to a single element of the set B through the function f.
If x is any number belonging to set A, so x is called independent variable. If y is any number in the set B, then y is called dependent variable. In other words, the independent variable has its values determined by domain gives occupation, and the values of variabledependent are found in the counter-domain.
The independent variable is known as such because its values do not depend on another.
variable or the rule of occupation to exist. Its values only need the definition of the domain of the function. The values of the dependent variable, as the name already indicates, depend on the function's formation rule and domain values.Domain
given to occupation:
f: A → B
y = f(x)
O set A is the domain of the function f. This set is formed by all the numbers that can take the place of x in the law of formation of the function, if x is the letter chosen to represent the variableindependent.
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All elements that belong to the domain of a occupation are dominant in it, that is, their values determine the values of the other variable. Because of this, this name was chosen for this set.
Example:
f: N → Z
y = x2
The domain of this function is the set of natural numbers. Therefore, the numbers that can be put in place of x, to find their respective values in the counter-domain, they are:
N = {0, 1, 2, 3, 4, 5, …}
dominion
given to occupation:
f: A → B
y = f(x)
Your counter-domain is set B. This set is formed by the elements that can take the place of y in the law of formation of the function, if y is the letter chosen to represent the dependent variable.
All values that belong to the counter domain of the occupation can be related to a value of the domain, but it can also happen that not all elements of the counterdomain are related to some element of the domain.
Example:
f: N → Z
y = x2
In this role, the elements that belong to the set From numberswhole and that are related to some element of the domain are just the perfect squares.
{0, 1, 4, 9, 16, 25, …}
Note that the negative numbers, although they are in the counter-domain, were not "used" in this occupation.
Image
the image of a occupation it's the set of all the numbers of the counter-domain that are related to some element of the domain. Example:
f: N → Z
y = x2
THE Image of that occupation it is just the set of perfect squares.
By Luiz Paulo Moreira
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
SILVA, Luiz Paulo Moreira. "Domain, co-domain and image"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/dominio-contradominio-imagem.htm. Accessed on June 28, 2021.
