A relation is a relationship between sets of values. In math, the relation is between the x-values and y-values of ordered pairs. The set of all x-values is called the domain of the relation, and the set of all y-values is called the range of the relation.
A relation from a set X (domain) to a set Y (range) is called a function if each element of X is related to exactly one element in Y.
A. A relation {(2,-3), (3,-3), (1,4), (9,2)} is a function, because each x has exactly one element y related to.
B. A relation {(8,-3), (3,8), (9,4), (-2,2)} is a function, because each x has exactly one element y related to.
C. A relation {(1,-1), (4,8), (9,-1), (3,2)} is a function, because each x has exactly one element y related to.
D. A relation {(1,-1), (-1,5), (1,-6), (-3,2)} is not a function, because x=1 has two possible outcomes y: y=-1 or y=-6.
Answer: A, B and C are functions and D is not a function
