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) Clearly, every element of domain is related to unique element of co-domain, so it is a function. 

Domain = {2, 5, 8, 11, 14, 17} 

Range = {1} 

(ii) Clearly, every element of domain is related to unique element of co-domain, so it is a function. 

Domain = {2,4, 6, 8,10,12,14} 

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

(iii) 1 is related to two elements of co-domain, namely 3 and 5, so it is not a function.