Consider the following variables where one is the final exam
score for a student on the departmental final exam and the 
other is his/her semester grade. Which of the following 
statements best describes their relationship to each other? 
In each case, explain why you exclude or include the choice. 

If y is a function x, then a corresponding value of y can 
always be determined just by knowing a a value of x.

-An individual's final exam score is a function of his or 
her semester grade.

False.  You certainly cannot determine what a student's 
final exam grade is just by knowing the semester grade. 

-An individual's semester grade as a function of his/her 
final exam score.

False.  You cannot determine what a student's semester grade 
is just by knowing the final exam score. (You would also 
have to know the grades on other tests, quizzes, projects, 
and homework.) 

-Each is a function of the other.

Certainly not.

-Neither is a function of the other.

This is the only true statement of the four in normal cases.

[The first three would be true and the last one false 
if and only if the only grade a student receives for the 
semester is the grade made on the final exam.  Incidentally 
I took a graduate course once where this was the case!!]

Edwin