The formal definition of a function states that:
"A function relates each element of a set with exactly
one element of
another set (possibly
the same set)."
The part that says "..with exactly one element.." means that for every
input (x-coordinate), it cannot return 2 or more values (y-coordinate). In other words, among the relations stated, we just have to look for the relation with repeating x-coordinates to find the relation that is not a function.
{(0, 0), (1, 0), (2, 0)} has no repeating x-coordinates so it is a function.
{(1, 2), (3, -5), (-1, 7)} has no repeating x-coordinates so it is a function.
{(7, -1), (3, -2), (5, -2)} has no repeating x-coordinates so it is a function.
{(-1, 3), (4, 2), (-1, 5)} has 2 pairs of "-1" x-coordinates so it is NOT a function.
