As according to given statement:
1). Each school has one principal so as there is a relation between school and principal so it is a function.
2). Each student has a unique student ID number: so as there are so many students and they allhave different unique student ID's so there is a function.
3). Shoe manufacturers make different type of shoes : so as there is relation but we can't describe a function between them.
4). Each month of the year has a total amount of rainfall measured in inches:
So it is a function between month and the rainfall measured in inches.