Final answer:
The set S {(0,1), (-3, 5), (4, -2), (-7, 5)} is a function because each x-value is unique and maps to only one y-value; thus, no x-values are repeated. The fact that points may create any kind of line or the order of x-values is irrelevant to it being a function. Option A is the correct answer.
Step-by-step explanation:
The set S given as {(0,1), (-3, 5), (4, -2), (-7, 5)} is being evaluated to determine if it represents a function. A function is a relation in which each input (or x-value) has exactly one output (or y-value). In the context of this question, the key factor to consider is whether any x-value is repeated with a different y-value.
Looking at the set S, we observe that each x-value is unique; that is, there are no repeated x-values paired with different y-values. This matches the definition of a function, which stipulates that each x-value should map to only one y-value. Therefore, we can conclude that S is a function based on the given points.
Option a states, 'S is a function because no x-values are repeated.' This is indeed the correct interpretation and the reason why S is a function. The other options are incorrect because whether the points create a straight line, have repeated y-values, or the x-values are not in increasing order does not affect the definition of a function.
The final answer is: a. S is a function because no x-values are repeated.