Y= {(2, 6), (3, 1, 4), (1), (5, 6)} is y a function and why?

If a set of points is a function, the elements of the set must have the same number of elements.

For example, if the function is from A→B, the elements must be ordered pairs.

So Y is not a function.



If Y is in fact  {(2, 6), (3, 1), (4, 1), (5, 6)}

then Y is a function, because each of the first coordinates appears only once.

In functional notation, we have f(2)=6, f(3)=1 etc

remark: if a first coordinate is repeated, for example if we have (2, 6) and also (2, 8)

this would mean f(2)=6, but also f(2)=8, which means f is not a function.