Question

4. Which set of ordered pairs represents a function?

(1) {(0,4), (2,4),(2,5)}
(2){(6,0), (5,0),(4,0)}
(3) {(4,1),(6,2), (6,3), (5,0)}
(4) {(0,4),(1,4), (0,5),(1,5)}​

Answer 1

Answer: (2) {(6,0), (5,0),(4,0)}

It is a function, where each value is associated with exactly one output.

Explanation:

A relation is said to be a function if the first components of the ordered pairs are associated with exactly one value of the second components of the ordered pair.

(1) {(0,4), (2,4),(2,5)}

here 2 is associated with 2 different values of second component.

Thus it is not a function.

(2) {(6,0), (5,0),(4,0)}

It is a function, where each value is associated with exactly one output.

(3) {(4,1),(6,2), (6,3), (5,0)}

It is not a function as 6 is associated with 2 different values of second component.

(4) {(0,4),(1,4), (0,5),(1,5)}​

It is not a function as 0 and 1 are associated with 2 different values of second component.