Final answer:
Adding either coordinate pair A. [-3,2) or B. (-3,2] to the set {(-3,7), (1,5), (4,13)} would prevent it from representing a function because these pairs have an x-value of -3, which is already associated with a different y-value in the set.
Step-by-step explanation:
A function is defined in mathematics as a relation where each element in the domain (set of inputs) is associated with exactly one element in the codomain (set of possible outputs). The set of coordinate pairs given by the student initially is {(-3,7), (1,5), (4,13)}, which is indeed a function since there are no repeated x-values with different y-values.
When considering which coordinate pair would prevent this set from representing a function, we must look for a coordinate pair that has the same x-value as one of the existing coordinates but a different y-value. The coordinate pairs provided as options are: A. [-3,2), B. (-3,2], C. [-2,7), and D. (-2,7). Both A and B have an x-value of -3, which is already present in the original set but associated with a different y-value (7). Therefore, adding either [-3,2) or (-3,2] would result in the same x-value (-3) being associated with two different y-values (7 and 2), which violates the definition of a function.
On the other hand, options C and D have an x-value of -2, which is not yet present in the original set of coordinates, so adding either of these pairs would not prevent the set from being a function.