A relation is any set of ordered pairs. The set of all first elements of the ordered pairs is called the domain of the relation, and the set of all second elements is called the range. function is a relation or rule of correspondence between two elements (domain and range) such that each element in the domain corresponds to exactly one element in the range. To further understand function, let’s study the following. Given the following ordered pairs, which relations are functions?
A = {(1,2), (2,3), (3,4), (4,5)}
B = {(3,3), (4,4), (5,5), (6,6)}
C = {(1,0), (0, 1, (-1,0), (0,-1)}D = {(a,b), (b, c), (c,d), (a,d)}
You are right! The relations A and B are functions because each element in the domain corresponds to a unique element in the range. Meanwhile, relations C and D are not functions because they contain ordered pairs with the same domain [C = (0,1)and (0,-1), D = (a,b) and (a,d)].
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