Question

Which of the following relations are functions? Give reasons. If it is a function determine its domain and range.

(i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

(ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

(iii) {(1, 3), (1, 5), (2, 5)}

Answer 1

(i) Here the relation is

{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}

All values of x are distinct. Each value of x has a unique value of y.

So the relation is a function.

$\therefore$ Domain of function = {2, 5, 8, 11, 14, 17}

Range of function = {1}.

(ii) Here the relation is

{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}

All values of x are distinct. Each value of x has a unique value of y.

So the relation is a function.

$\therefore$ Domain of function = {2, 4, 6, 8, 10, 12, 14}

Range of function = {1, 2, 3, 4, 5, 6, 7}.

(iii) Here the relation is

{(1, 3), (1, 5), (2, 5)}

This relation is not a function because there is an element 1 which is associated to two elements 3 and 5.