 Hi and how are you all today? I am Priyanka and let us discuss the following question. It says which of the following relations are functions? Give reasons. If it is a function determine its domain and range. These are the three sub-parts of the question which are given to us and first of all in the question we need to tell whether the given part is a function or not and then if it is find the domain and its range. But first we let this first clear what does a function means. A relation from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. Further it implies that no two ordered pair in F have the same first element. For determining its domain and range we will be defining the domain as a set of all the first elements of the ordered pair which belongs to the function and range is the set of the second element of the ordered pair that belongs to the function. Now this definition will be more clear to you when we will be proceeding on with our solution and the knowledge of what a function is all about is the key idea that we are going to use in order to proceed on with our solution. Now for the first part we are given the ordered pair as 2, 1, 5, 1, 8, 1, 11, 1, 14, 1 and 17, 1. Now we have to determine whether it is a function or not. From the definition of a function we know that no two ordered pair of the function should have the first same element. Now here the first element of the ordered pair in the relation are 2, 5, 8, 11, 14 and 17 which are all different from each other. Therefore the given relation is a function. Given the reason in words we see that we see that no two ordered pair in the relation the same first element. So therefore the given relation is a function. Got it? Again according to the definitions of domain and range are the first elements of all the ordered pair that is 2, 5, 8, 11, 14 and 17. Whereas range being the set of all the second elements of the ordered pair if you carefully see all the second element of these ordered pair is the same number that is 1. So range is a set of one element that is 1. So this completes the first part of the question. Preceding on to the second part here the relation given to us is the ordered pairs of 2, 1, 4, 2, 6, 3 and so on. Now here the first element of the ordered pair in the relation are 2, 4, 6, 8, 10, 12, 14 which are different from each other. So hence the given function the given relation is a function. Here all the first components you can write a similar word similar sentence in different using different words also but it means the same. Here all the first components of the ordered pair in relation are different right? Therefore is it a function or not? Yes you are right. Therefore the given relation is a function. And now we need to find the domain and what definition did I give you for domain? It's the right. It's the set of all the first elements of the ordered pair which are having a green tick over them so that is 2, 4, 6, 8, 10, 12 and 14. Whereas range is a set of all the second elements of the ordered pair. So we have 1, 2, 3, 4, 5, 6 and 7 in it. So this completes the answer of the second part. Moving on to the third part we are given the relation as the ordered pair 1, 3, 1, 5 and 2, 5. Now here since 2 ordered pair the same first element that is 1, 1 therefore the given relation is not a function. Right? This ends our second part since it's not a function we do not need to find the range and domain. So for solving the given problem we use the definition of function if no two ordered pairs in a relation have the same first component it is a function or otherwise it's not. So I hope you enjoyed the session. Bye for now. Take care.