Question

Is {(1, 2); (2, 3); (3, 4); (2, 5)} a function?

Answer 1

No it is not a function.

Explanation:

A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.

The definition is often stated as: A relation in which every `x` value is associated with exactly one `y` value. "Exactly one means one but two or more:

`{(1, 2); (2, 3); (3, 4); (2, 5)}` includes the points `(2,3)` and `(2,5)`. Therefore this set of pairse is not a function.

Note

`{(0,1), (1,3), (2, 5), (3, 5)}` is a function.
(It is ok to have different first elements and the same second elements. The definition of function is very precise.)