 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, Draw the graph and determine the intervals on which the function f of x is equal to absolute value of x minus 5 the whole minus 4 is increasing and decreasing. Let us start with the solution of the given question. We have to find the intervals for which the given function is increasing and decreasing. First we graph the function f of x is equal to absolute value of x minus 5 the whole minus 4. We see that its parent graph is absolute value of x. If we translate it h units horizontally and k units vertically, we get absolute value of x minus h the whole plus k. Thus we see that f of x is equal to absolute value of x minus 5 the whole minus 4 is of type absolute value of x minus h the whole plus k. On comparing we get h is equal to 5 and k is equal to minus 4. Thus we obtain the graph of the function f of x is equal to absolute value of x minus 5 the whole minus 4 by translating the parent function that is f of x is equal to absolute value of x, 5 units right horizontally and 4 units down vertically. This is the graph of the function that is absolute value of x. Now if we move it 4 units down that is 1, 2, 3, 4 and 5 units right that is 1, 2, 3, 4, 5 we get the graph of the function f of x is equal to absolute value of x minus 5 the whole minus 4. Now we have to find the intervals in which it is increasing and decreasing. We see that the values of f of x are decreasing for x less than 5 and thus the curve is moving downwards. Also the value of f of x are increasing for x greater than 5 and thus the curve is moving upwards. Thus the function f of x is equal to absolute value of x minus 5 the whole minus 4 is decreasing for x is less than 5 and increasing for x is greater than 5. So x is equal to 5 is the critical point thus when x belongs to the open interval minus infinity to 5 f of x is decreasing and when x belongs to the open interval 5 to infinity f of x is increasing. This is the required answer. This completes our session. Hope you enjoyed this session.