They differ by just one number, but only one is a function. It represents the values that can be plugged into the function to obtain a valid output. The domain of a function refers to the set of all possible input values for which the function is defined. If each number in the domain is a person and each number in the range is a different person, then a function is when all of the people in the domain have 1 and only 1 boyfriend/girlfriend in the range.Ĭompare the two relations on the below. Domain and range are two fundamental concepts in mathematics that are used to describe the input and output of a function, respectively. Some people find it helpful to think of the domain and range as people in romantic relationships. Gino below, has more than 1 student in a classroom.Ī way to try to understand this concept is to think of how mothers and their daughters could be represented as a function.Įach element in the domain, each daughter, can only have 1 mother (element in the range). If we put teachers into the domain and students into the range, we do not have a function because the same teacher, like Mr. Therefore, relation #2 does not satisfy the definition of a mathematical function. On the other hand, relation #2 has TWO distinct y values 'a' and 'c' for the same x value of '5'. Since relation #1 has ONLY ONE y value for each x value, this relation is a function. In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value. Like a relation, a function has a domain and range made up of the x and y values of ordered pairs.
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