 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that a function y is equal to p of x is defined by graph below. This is the graph of the function y is equal to p of x. Draw the graph of y is equal to p of x plus 2 the whole minus 2. We know that vertical translation of a function is given by y is equal to f of x plus k where k is constant. If the value of k is greater than 0 then the graph of the function is shifted upwards by k units. And if the value of k is less than 0 then the graph of the function is shifted downwards by k units. Similarly horizontal translation of a function is given by y is equal to f of x minus k the whole where k is constant. And if the value of k is greater than 0 then the graph of the function is shifted to right by k units. And if the value of k is less than 0 then the graph of the function is shifted to left by k units. With this key idea we proceed to the solution. Now we are given the graph of the function given by the equation y is equal to p of x. And we have to draw graph of y is equal to p of x plus 2 the whole minus 2. From the key idea we know that f of x minus k the whole is horizontal translation. So here horizontal translation is given by p of x plus 2 the whole. On comparing we get the value of k as minus 2. Now we have k is equal to minus 2 which is less than 0. So the graph will be shifted 2 units to the left. Now this red curve is the horizontal shift. Also from the key idea we know that f of x plus k is vertical translation. And here we are given the function p of x plus 2 minus 2. So here minus 2 is the unit of translation since here minus 2 is less than 0. So graph will be shifted 2 units vertically downwards. So now we translate this curve vertically that is we move the horizontally translated curve 2 units down. So we get the following graph. Here this brown curve shows vertical translation and thus the brown curve is the graph of the function given by the equation y is equal to p of x plus 2 the whole minus 2. And this is the required graph. This completes our session. Hope you enjoyed this session.