 Hello and welcome to the session. In this session, we will learn about functions and their representation. And let us see what are functions. Let A be between non-empty sets when a function are mapping from A to B as a rule which associates every element X to a unique element Y of set B. Then we write is a function from A to B such that Y is equal to F of X where Y belongs to B. So here Y is called the image of X and is denoted by. Now the set of different values of X is called domain of a function. The set of different values of Y are range of a function. Now a relation from A to B is a function of elements of set A. Our user is not with more than one element of set B. Now to illustrate this, let us discuss one example in which in the first part our one is the relation from A to B. In the second part R2 is the relation from C to D and in the third part R3 is the relation from E to F. And all of them are represented with the arrow diagram. Now we have to examine which of them are functions and which are not. Now if any of the relations were satisfied these two conditions then that relation will be a function. Now in the first part our one is the relation from A to B but here we can see set A are not used up. That is 3 which is the element of set A is not used up. That means it is not connected with any of the elements of set B. The relation R1 is not a function. R2 is the relation from C to D with D and E which are the conditions for a function of function. Now in the third part from E to F now here we set E is not connected with more than one element. That is using one element of both the conditions for a function therefore how to represent a function. Now a function can be represented in Roster form by arrow diagram by equation in set B form represented by a graph. Which is equal to the set containing the oddity pairs 0 minus 14 which is present this function. Now we can write the oddity pairs 0 minus 1 1 4 3 14. Now let us represent the given function by the arrow diagram. Now given oddity pairs 0 minus 1 3 14. Representing the given function with the help of arrow diagram first of all we will draw two rectangles. We will write the first components of all the oddity pairs in the given function. So these are the first components of all the oddity pairs 0 1 2 oddity pairs in the given function. Which are minus 1 4 9 and 4. Now 0 is related with minus 1 so we will connect 0 and minus 1 with the help of an arrow. Now 1 is related with 4 so we will connect 1 with 4. We will connect 2 with 9 and 3 with 4. Now f is a function so we are having different. For these different values of x we are going to tender the different values of y. And y is equal to in the equation for the function x minus 1. Now these are the different values of x equal to 5 x minus 1 will be equal to 5 into 0 minus 1 which is equal to 0 minus 1 and the oddity pair 0 minus 1. Which is this oddity pair in the given function. So satisfy the rule of the relation plus then the given function represented as oddity pair xy. y is equal to 5 x minus 1. This is the representation of the function if that will reform. Now let us do 7 functions by a graph. Now given in the ordered pairs 0 minus 1 1 4 we will plot these points on the graph. Let us plot the point 0 minus 1. So this is the point 0 minus 1 on the graph. Point 1 4 point 1 4 on the graph. So we have plotted and by drawing all these points we are getting the graph of the given function which is represented by the equation y is equal to 5 x minus 1. So in this session we have learnt about as methods of representing functions. So this concludes our session hope you all have enjoyed the session.