Final answer:
Both Situation A, pairing student names with favorite colors, and Situation B, pairing student names with favorite math teachers, represent functions because each student's name is associated with exactly one output in each scenario.
Step-by-step explanation:
The question asks which set represents a function, given two situations: A, which pairs a student's name with their favorite color, and B, which pairs a student's name with their favorite math teacher. In mathematics, a set represents a function if each input (in this case, a student's name) is associated with exactly one output (either a favorite color or a favorite math teacher).
For Situation A, it is possible for a student to have only one favorite color, thus each student's name (input) would correspond to only one color (output). This suggests that Situation A represents a function. Similarly, for Situation B, a student is likely to have one favorite math teacher, meaning each student's name would correspond to only one math teacher. This also suggests that Situation B represents a function.
The correct answer is C, both A and B, because in both scenarios, each student's name is associated with only one color or one teacher, respectively, satisfying the definition of a function.