Respuesta :
Given two sets X and Y, a relation between X and Y freely associates elements of X with elements of Y, with no restrictions.
A function is a relation with some restrictions: there must be exactly one element of Y connected with each element of X.
The set X is called the domain of the function, and it represents all the possible inputs that we can feed the function with. As we just said, every element of the domain must have a correlated element in Y.
The set Y is called the range of the function, and it represents all the possible outputs that the function can return.
The difference between function and relation and the relationship between the domain and the range of a function is discussed below
What is domain and range?
The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
Let there be an X set and a Y set. An ordered pair (x,y) is called a relation in x and y. The first element in an ordered pair is called the domain, and the set of second elements is called the range of the relation.
A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range.
For example, each person is in the following table is paired with a number representing his or her height:
Alex → 180 Claudia → 165 Gilbert → 204 Judith → 165
The given relation {(Alex, 180), (Claudia, 165), (Gilbert, 204), (Judith, 165)} is a function as every person is pairs with exactly one number, their height. The domain is (Alex, Claudia, Gilbert, Judith). The range is (165, 180, 204).
The domain is the input, the independent value—it's what goes into a function. The range is the output, the dependent value—it's what comes out. Domain and range may be limited to a few discrete values, or they may include all numbers everywhere, to infinity and beyond.
learn more about domain and range here:
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