Question

Which of the following relations is a function?

Answer 1

(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.