To determine which of the given situations represents a function, we need to recall the definition of a function in mathematics. A function is a relation in which each element of the domain (input) is associated with exactly one element of the codomain (output).
Let's analyze each situation:
Situation A: (Student's name, all the colors that the student likes)
- Here, a student’s name (domain) is associated with all the colors that the student likes (codomain).
- Since a student can like multiple colors, a single student’s name can be associated with multiple colors.
Based on the definition of a function, Situation A does not represent a function because there isn't a one-to-one association; a single element in the domain can be mapped to multiple elements in the codomain.
Situation B: (Student's name, the student's favorite math teacher)
- In this situation, a student’s name (domain) is associated with the student’s favorite math teacher (codomain).
- Each student can only have one favorite math teacher at any given time.
Given the definition of a function, Situation B does represent a function since each student’s name is associated with exactly one favorite math teacher, thus ensuring a one-to-one association.
Therefore, based on this analysis:
- Only A is not correct because Situation A does not satisfy the criteria for a function.
- Only B is correct because Situation B does satisfy the criteria for a function.
- Both A and B is not correct because only Situation B is a function.
- Neither A nor B is not correct because Situation B is a function.
Thus, the correct answer is:
Only B
