Which of the following relations is a function?

(2,5), (3,5), (2,9), (1, 10)

(1,3), (2,9), (3, 7), (4,3)

(0,6), (0, - 9), (-9,-6), (8,-4)

(3,5), (3,7), (3,9), (3, 11)

(1,3), (2,9), (3, 7), (4,3) is a function

Solution:

A function is a relation in which each element of the domain is paired with exactly one element of the range.

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y.

The domain is the set of all the values of "x". The range is the set of all the values of "y"

(2,5), (3,5), (2,9), (1, 10)

Here domain = {2, 3, 2, 1} and range = {5, 5, 9, 10}

In the domain, the value 2 is paired with both 5 and 9. So, this relation is not a function.

(1,3), (2,9), (3, 7), (4,3)

Here domain = {1, 2, 3, 4} and range = {3, 9, 7, 3}

In the domain, each element of the domain is paired with exactly one element of the range. So, this relation is a function.

(0,6), (0, - 9), (-9,-6), (8,-4)

Domain = {0, 0, - 9, - 8} and range = {6, - 9, - 6, - 4}

In the domain, the value 0 is paired with both 6 and - 9. So, this relation is not a function.

(3,5), (3,7), (3,9), (3, 11)

Domain = {3, 3, 3, 3} and range = {5, 7, 9, 11}

In the domain, the value 3 is paired with 5, 7, 9, 11.

So, this relation is not a function.