That is part of the definition of a function.
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Not every relation is a function. But every function is a relation. Function is just a part of relation.
A Function
When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").
A relation is a function if every value in the domain is mapped to only one value in the range. A non-mathematical example is mothers. Leaving aside surrogacy, every person has only one mother. Therefore the relation f(x) = x's mother is a function. But f(x) = x's ancestor is not a function because everyone has loads of ancestors. They may not all be known but that is not relevant.
If a relation can be called a function, it means that the relation maps every element to one and only one other element. If you have some ordered pairs and see that, for example, 1 maps to 4 (1,4) and 1 also maps to 7 (1,7) , you don't have a function.