Question

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.

1. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
2. {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
3. {(1, 3), (1, 5), (2, 5)}

Answer 1

1. Let R = {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} This relation is a function because the first element of any two ordered pairs is not equal. Domain = {2, 6, 8, 11, 14, 17} and range = {1}
2. Let R = {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} It is a function because the first element of any two ordered pairs is not equal. Hence, domain = {2, 4, 6, 8, 10, 12, 14}, range = {1, 2, 3, 4, 5, 6, 7}.
3. It is not a function because (1, 3), (1,5) have the same first element.