 So, quickly draw the graph of question number 5 of your worksheet. Y is equal to negative 1 by x minus 3 minus 4. Go step by step, start with the skeleton graph, then see what transformation you should start applying onto that function. It's a negative 3 meaning should you shift it to the left? Yeah, it's the same thing. It means the same thing as doing this, y plus 4 is equal to negative 1. It's the same thing. There's no difference between these two. Then, who is that? Both the arms will simultaneously move. See, the graph, it's like it is my two arms. If you shift me, both my arms will move, isn't it? It's not like this arm will leave there and I'll move like this, correct? They're connected. So, where I go? What's the number? Both will move by the same. Both will move by the same, same amount, wherever you... Getting the 1. I'm not saying it right. Both arms? The entire graph will move to the left. If it's in x minus 3, what do you form? Whether it's 1 by x 4, it doesn't make a difference. I got it. I don't know what you mean by negative. Now here, we're going to make a negative. Because we're making negative either x is negative or just y is negative. I want the whole thing to become negative. Before you do the x minus. That's why the order becomes important. That's what I was explaining to you. You have to change the sign. Because after changing y with y plus, you cannot change the sign there. Then if you change y with change, if at all you're changing that. Seanach, right? Seanach. Seanach. Okay. Ronach, Seanach. Okay. Yeah. Let's go step by step. All of you please pay attention to this. Should I replace the sign of x right now? Why x? Why your x doesn't matter actually. If I change my sign of y or if I change my sign of x, does it really bring any difference to my final order? So if you reflect its axis, you can check it out. So you want to change the sign of x. Okay, let's follow this. So what will be the graph for this then? Changing the sign of x means reflecting the graph of all. Let me choose. Is that fine? So blue one is now the graph of y is equal to. So you have to change both arms. Both arms. That's why I told you no. It's like this, let's say. And you're making me like this. Both arms will change. So y is equal to negative 1 by x is done. What next? Minus 3. Should I change my x with x minus 3? Yeah. So when I change my x with x minus 3, shift it to 1. I will shift this blue graph. See you missed the right. I missed the. Understood? So if I'm shifting it to the right, now tell me. Will it change the horizontal asymptote or will it change its vertical asymptote? Horizontal asymptote. Vertical asymptote. Understood? Is this understood? So you are shifting this blue graph 3 units to the right. That means now, instead of having y axis as the asymptote or instead of having x equal to 0 as the asymptote, now you knew asymptote x equal to 3. Understood? Now, what next I have to do? How would I replace y with y plus 4? If you change your y with y plus 4, the same graph will go down by 4 units. So what will change? Will it change its horizontal asymptote in red color? I'm drawing it on the same graph so it may look a bit hush-push. But now this is your y is equal to negative 4 line. So ultimately, I'm drawing a miniature over here. Your graph will look like this. Understood? I will show you step by step on GeoG graph. Okay. y is equal to 1 by x. So what I mean about it? Is that right? Is that right? Now, first step that we did was, we changed x as negative x. Correct? So what I will do is, I will change x with x minus 3. The previous one. Shifted 3 units to the right. Now your new asymptote is equal to 3 lines. You see this line? This line will be asymptote means this will appear to touch the curve at infinity. Okay? Hide this also. Don't need this. Now, I'm changing y with y plus 4. I'll make the change here itself. You see that? It went down. Now this line that you see, y is equal to minus 4. That will be your horizontal asymptote. And x equal to 3 will be your vertical asymptote. Understood? Understood. This missing part is because of the graphic issue. Understood how it works? Understood what is happening. So what is happening is, from this position it is now, this asymptote has shifted 3 units to the right and this asymptote has shifted 4 units down. So something like this is happening. So you can just plot a graph. The turning point is 3 comma minus 4. There's no turning point here. I'll talk about it. Okay? Is this fine? Okay. Quickly without wasting much time, we can talk about, yeah somebody had a question here. How do you plot this? This all will become like this. Somebody asked, somebody said very correctly, it will be the same as 1 by x. The same 1 by x. Now, y is equal to 1 by x square. Of the given one. First. Is this fine? Let me just reopen it again. 1 by x and 1 by x cube is equal to 1 by x cube. Do you see the difference? Now again the difference is, after 1 and before minus 1. Now see what is happening over here. Of course at 1 and minus 1, both of them will give you the same value. Correct? What is happening? After what? The graph is the, is the, is the highest one, isn't it? But equal to half. So y is equal to 1 by half, which is 2. And y is equal to 1 by half cube, which is 8. Which is more? 1 by x cube is more. So you can see that the blue graph dominates 1 by x. The blue is the graph of this one. This is your blue graph. So between 0 and 1, who is the boss? 1 by x cube. Yes or no? 1 by x. That's what is happening. So value wise, magnitude wise, the graph of 1 by x is higher than the graph of 1 by x cube when you are 2 minus 1. Between minus 1 to 1, the graph of 1 by x cube will have a higher value than graph of 1 by x. Simple? Aja, what will happen if I plot 1 by x to the power 5? Do one thing. On your notebook, draw the graph x cube 1 by x to the power 5 on the same x y coordinate system. And clearly show me what will happen. And if you have done this, 1 by x cube, 1 by x cube, all are powers. I will go to 1 by x square also. This is the graph of 1 by x 5. Absolutely correct. Done? Wonderful. Okay, draw both the arms. Most of you are just drawing single arms. It's okay. I'm not too keen on its beauty of the graph. I just want to see the relative positioning. Which is what, my dear? 1 by x 5, 1 by x cube, 1 by x cube. Oh, okay. Do you realize that 1 by x... Let's see whether it is happening like this. Where is my... y is equal to 1 divided by x to the power of 5. You see that? Right one. Understood? How it works? A similar nature you would have on the x square and 1 by x to the power 4 and 1 by x to the power 6 and 1 by x to the power 8 like that. It's the same change in the curvature that you will also see there also. So can I show you there? So let's delete them. The interval is all the same. The interval is the same. 1 and minus 1 are the critical points for you. So y is equal to 1 divided by x square. Okay, this is the graph. Next, y is equal to 1 divided by x 4. You see that? Again, 1 and minus 1 are the points to be careful about. So it is more flatter. Correct? What about 1 by x to the power 6? Let's see that. y... y is equal to 1 divided by x to the power of 6. Even more flatter. Correct? So after 1, 1 by x to the power 6 is the least. Between 0 and 1, 1 by x to the power 6 is the highest. Are you getting this point? Okay. So please plot. Please plot. Question number 7. Now don't get scared by that negative 2. That will not... Question number 6. Oh sorry, question number 7. Question number 7, my bad. What question number 7?