Final answer:
Upon examining the set S = { (4, -5), (12, 5), (-8, 10), (7, 0)}, since each x-coordinate is unique and only paired with one y-coordinate, the set S qualifies as a function.
Step-by-step explanation:
To determine if a set S is a function, we need to check whether each input value, or x-coordinate, maps to exactly one output value, or y-coordinate. In other words, no x-value should be associated with more than one y-value in the set. Looking at the set S = { (4, -5), (12, 5), (-8, 10), (7, 0)}, we see that each x-coordinate is unique and is paired with exactly one y-coordinate. Therefore, the set S is indeed a function