 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that, consider the function defined by the equation y is equal to minus 2 into f of 1 by 2 into x plus 5 the whole and this complete whole minus 3. Now the first part of the question says if the function is written in the form y is equal to a into f of b into x minus h the whole and this complete whole plus k states the values of a, b, h and k and the second part says write the transformations associated with the parameters a, b, h and k. We know that given any function y is equal to f of x then y is equal to a into f of b into x minus h the whole plus k affects the graph in following ways. Now a causes the graph of the function to stretch when a is greater than 1 or to compress when 0 is less than a is less than 1 vertically by factor a and if a is less than 0 that is there is a negative sign before the given function then the graph is reflected over x axis. Similarly b causes the graph of the function to stretch when 0 is less than b is less than 1 or to compress when b is greater than 1 horizontally by factor 1 upon b and if b is less than 0 then the function is reflected over y axis. Similarly h causes the graph to translate horizontally also if h is greater than 0 then curve moves to right and if h is less than 0 then the curve moves to left. Similarly k causes the graph to translate vertically if the value of k is greater than 0 then the curve moves upwards and if k is less than 0 then the curve moves downwards. With this key idea let us proceed to the solution. We are given this equation that is y is equal to minus 2 into f of 1 by 2 into x plus 5 the whole this complete whole minus 3. In the first part of the question we are given this function written in the form of y is equal to a into f of b into x minus h the whole this complete whole plus k we have to find values of a b h and k. Now on comparing these two equations we get the value of a as minus 2 the value of b as 1 upon 2. Now to find the value of h we can write x plus 5 as x minus of minus 5 which is of the form x minus h. So now when we compare x minus of minus 5 with x minus h we get the value of h as minus 5 thus h is equal to minus 5 and k is equal to minus 3. Now in the second part of the question we have to write the transformations associated with parameters a b h and k. So by using the idea here we have modulus of a that is modulus of minus 2 which is equal to 2. So modulus of a is equal to 2 which is greater than 1. So there is a vertical stretch by factor 2 also the value of a is equal to minus of 2 which is less than 0. So the graph is reflected over x axis and we have the value of b as 1 upon 2 that is b is equal to 1 upon 2 and 1 upon 2 lies between 0 and 1. So there is a horizontal stretch by factor 1 upon b that is 1 upon 1 by 2 the whole which is equal to 2 and we have just found out the value of h as minus 5 which is less than 0. So graph is translated horizontally to the left by 5 units and lastly the value of k is equal to minus of 3 which is again less than 0. So the graph is translated vertically down by 3 units. Thus we have the following transformations first vertical stretch by factor 2, second reflection over x axis, third horizontal stretch by factor 2 and fourth translation of 5 units left and 3 units down which is the required answer. This completes our session. Hope you enjoyed this session.