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# What is the difference between a function and a relation?

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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.

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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.

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## Related Questions

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In math, a relation describes how elements from one set, A, are related to elements of a second set, B, in terms of ordered pairs (x,y). For example, in a set of ordered pairs, the x-values can be the elements from set A and make up the domain. The y-values can be the elements from set B and form the range.

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The domain of a function is all of the x values of the function without any repetition. A vertical line has only one x value as its domain, while a horizontal line has a domain of all x values.

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The domain for a function is all of the acceptable values for x where the y value is both a real and a defined number. All values of x are acceptable for a quadratic equation, and therefore the domain is all real numbers.