Can someone help and explain Find the domain and range of the following relation. Determine if the relation is a function and explain

domain-and-range

#1

can someone help and explain Find the domain and range of the following relation. Determine if the relation is a function and explain: {(1,2), (3,3), (4,2), (5,6), (6,3)}

Answer:

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

Let us try to represent this relation in a diagram:

Set A Set B
1 -----------> 2
3 -----------> 3
4 -----------> 2
5 -----------> 6
6 -----------> 3

Or,
Set A Set B
(1,4) -----------> 2
(3,6) -----------> 3
(5) -----------> 6

set A has 5 elements- 1,3,4,5 and 6. Therefore the domain is {1,3,4,5,6}.

set B has 3 elements- 2,3 and 6. Therefore the domain is {2,3,6}.

To decide whether this is a function or not, we need to check if every element in set A has a unique image in set B or not. We can see by viewing the relation that the elements of set A- 1,3,4,5 and 6 are occurring only once that means they have their respective unique images. So this relation is a function.