A function is a mapping that maps each element of its domain (student's name) to exactly one element of its co-domain (favorite ...). Assuming student names are unique and the notion of "favorite" is exclusive (can't have two or more "favorites" of the same type), then both A and B describe mappings that are functions.
A function means each input goes to only one output. As long as each student is only entered once, and they only have one favorite color and one favorite math teacher, then A and B are functions.
