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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.
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Is the relation a function?
Not every relation is a function. But every function is a relation. Function is just a part of relation.
When does a relation be a function?
A function is a relation whose mapping is a bijection.
When can you say that the graph is function or mere relation?
If a vertical line intersects the graph at more than one point then it is not a function.
A relation is a special type of function?
No. A relation is not a special type of function.
What is the difference between function and a relation?
Good question. A relation is simply that; any x-value to create any y-value. A function, however, cannot be defined for multiple values of x. In other words, for a relation to be a function, it must have singular values for all x within its domain.
