Given the sets of ordered pairs, determine if they represent a relation or a function. If it is a function,specify the domain and range. (Criteria A)a) {(1,2),(2,3),(1,5),(4,6)}{(1,2),(2,3),(1,5),(4,6)}b) {(3,4),(2,7),(5,2),(3,1)}{(3,4),(2,7),(5,2),(3,1)}c) {(2,3),(5,6),(2,7),(8,1)}{(2,3),(5,6),(2,7),(8,1)}d) {(1,3),(2,5),(3,7),(4,9)}{(1,3),(2,5),(3,7),(4,9)}
Question
Given the sets of ordered pairs, determine if they represent a relation or a function. If it is a function,specify the domain and range. (Criteria A)a) {(1,2),(2,3),(1,5),(4,6)}{(1,2),(2,3),(1,5),(4,6)}b) {(3,4),(2,7),(5,2),(3,1)}{(3,4),(2,7),(5,2),(3,1)}c) {(2,3),(5,6),(2,7),(8,1)}{(2,3),(5,6),(2,7),(8,1)}d) {(1,3),(2,5),(3,7),(4,9)}{(1,3),(2,5),(3,7),(4,9)}
Solution
Sure, let's go through each set of ordered pairs:
a) {(1,2),(2,3),(1,5),(4,6)} This set of ordered pairs represents a relation because each first element (x-value) is paired with a second element (y-value). However, it does not represent a function because the first element '1' is paired with two different second elements '2' and '5'. In a function, each first element can only be paired with one second element.
b) {(3,4),(2,7),(5,2),(3,1)} This set of ordered pairs also represents a relation. But similar to the first set, it does not represent a function because the first element '3' is paired with two different second elements '4' and '1'.
c) {(2,3),(5,6),(2,7),(8,1)} This set of ordered pairs represents a relation. However, it does not represent a function because the first element '2' is paired with two different second elements '3' and '7'.
d) {(1,3),(2,5),(3,7),(4,9)} This set of ordered pairs represents both a relation and a function. Each first element is paired with only one second element. The domain (set of first elements) is {1,2,3,4} and the range (set of second elements) is {3,5,7,9}.
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