Which of the relations given by the following sets of ordered pairs is a function?
A.{(1, 1), (1, 3), (1, 5), (1, 7), (1, 9)}
B. {(2, 1), (7, 5), ( − 4, 0), (3, 1), (0, −6)}
C. {(2,7),(6,5), ( − 3, 9), (2, 0), ( − 5, 3)}
D. {(1, 2), (2, 3), (3, 4), (3, 3), (2, 2), (1, 1)}
B. {(2, 1), (7, 5), ( − 4, 0), (3, 1), (0, −6)} is a function because each input (first coordinate) is paired with only one output (second coordinate). For example, 2 is only paired with 1 and not with any other number in the set.
In contrast, A, C, and D are not functions because there are input values that are paired with multiple output values. For example, in set A, the input 1 is paired with 5 different output values (1, 3, 5, 7, and 9), violating the definition of a function.