Which of the following relations is/are function/s? a. x = {(1,2), (3,4), (1,7), (5,1)} b. g = {(3,2), (2,1), (8,2), (5,7)} c. h = {(4,1), (2,3), (2, 6), (7, 2)} d. y = {(2,9), (3,4), (9,2), (6,7)}

 Which of the following relations is/are function/s?

a. x = {(1,2), (3,4), (1,7), (5,1)} b. g = {(3,2), (2,1), (8,2), (5,7)} c. h = {(4,1), (2,3), (2, 6), (7, 2)} d. y = {(2,9), (3,4), (9,2), (6,7)}

To determine if the given relations are functions, we need to check if each input value (x-coordinate) in the relation corresponds to a unique output value (y-coordinate). If there is any input value that maps to multiple output values, the relation is not a function. a. x = {(1,2), (3,4), (1,7), (5,1)} In this relation, the input value 1 maps to two different output values, 2 and 7. Therefore, this relation is not a function. b. g = {(3,2), (2,1), (8,2), (5,7)} In this relation, each input value has a unique output value. Therefore, this relation is a function. c. h = {(4,1), (2,3), (2,6), (7,2)} In this relation, the input value 2 maps to two different output values, 3 and 6. Therefore, this relation is not a function. d. y = {(2,9), (3,4), (9,2), (6,7)} In this relation, each input value has a unique output value. Therefore, this relation is a function. Summary: The relations that are functions are: - Relation b: g = {(3,2), (2,1), (8,2), (5,7)} - Relation d: y = {(2,9), (3,4), (9,2), (6,7)}