 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that identify the series of transformations from graph A to graph C for function y is equal to modulus of x also write the function for graph C. Let us start with the solution of the given question. We are given the graph of the function y is equal to modulus of x which is denoted by this green curve called graph A. After a series of transformations this curve is transformed into graph C which is given by this pink curve. Now we shall identify the series of transformations graph A is transformed to graph B and then to graph C. Let us find the transformation from graph A to graph B first. See if we stretch this green curve vertically upwards then all the points will move further away from x axis and will become closer to y axis. Thus there is a vertical stretch and we got graph B. Now let us find the stretch factor. We know that when we stretch the graph by factor A the coordinates x, y change to the coordinates x, y. Now we see that the point with coordinates minus 1, 1 lies on graph A also on graph B for x is equal to minus 1 we have y equal to 3 so point with coordinates minus 1, 3 lies on graph B so transformed coordinates are given by minus 1, 1 transforms to the point with coordinates minus 1, 3. Now on comparing these two transformations we can write this coordinate as minus 1, 3 into 1 so we say that the value of A is 3 so here A is equal to 3 so we say that graph A is stretched by factor 3 to form graph B. Now from graph B we move to graph C. Now let us find the next transformation. Now we see graph B starts from origin with coordinates 0, 0 but the transformed curve of graph C starts from point 3, 1 which means this blue curve is shifted 3 units right and 1 unit up so there is a translation of 3 units right horizontally and 1 unit up vertically. Thus we have the following transformations from graph A to graph C that is vertical stretch of factor 3 next horizontal translation of 3 units right and vertical translation of 1 unit up. Now we have to write the equation for graph C we know that the transformed equation for any function given by y is equal to f of x is given by y is equal to A into f of B into x minus h the whole plus k where A is the vertical stretch, B is horizontal stretch, h is horizontal translation and k is vertical translation. Now here we know that A that is vertical stretch is equal to 3, B is equal to 1 as there is no horizontal stretch, h that is horizontal translation is equal to 3 and k which is vertical translation is equal to 1. So here we have the values of A as 3, B as 1, h as 3 and k as 1. So equation for graph C from the given function y is equal to modulus of x is given by y is equal to A that is 3 into f of B into x minus h the whole that is 1 into x minus 3 the whole which is x minus 3 plus k that is 1. Here we know that f of x is equal to modulus of x so f of x minus 3 will be given by modulus of x minus 3 that is we have replaced x by x minus 3 in the given function. So we can write this equation as y is equal to 3 into modulus of x minus 3 plus 1 this is the required equation this completes our session hope you enjoyed this session