Which of the following relations is not a function?

{ (0, 0), (1, 0), (2, 0) }

{ (-1, 3), (4, 2), (-1, 5) }

{ (1, 2), (3, - 5), (-1, 7) }

{ (7, - 1), (3, - 2), (5, - 2) }

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.