What Is the Difference Between a Function and a Relation?
A relation is a set of numbers that have a relationship through the use of a domain and a range, while a function is a relation that has a specific set of numbers that causes there to be only be one range of numbers for each domain of numbers. All functions are relations, but all relations are not functions.
There are numbers that are related to each other in every relation. There could be a large variety of numbers in the domain for a given range. For example, if x is equal to 23, then y could be equal to 46 or 11.5, depending on the factors that are being played into the domain.
In a function, the numbers will always be able to relate back to a single number out of the range of numbers. It can be concluded that if x equals 13, then y will always equal 26. There may be many numbers in a domain that lead to the same range in a function, but there will never be more numbers in a range than a domain. If the number of x changes to 14, then y will change to 28. Many mathematicians use the term "well behaved" for numbers that are part of a function.