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Show how the followlng transformations can be tchleved tilty 3teps Reii#:0h400HLlu Heot 41=#46t...

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Show how the followlng transformations can be tchleved tilty 3teps Reii#:0h400HLlu Heot 41=#46t

Show how the followlng transformations can be tchleved tilty 3teps Reii# :0h 40 0H Llu Heot 41=#4 6t



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Discuss: Obtaining Transformations Can the function $g$ be obtained from $f$ by transformations? If so, describe the transformations needed. The functions $f$ and $g$ are described algebraically as follows: $$ f(x)=(x+2)^{2} \quad g(x)=(x-2)^{2}+5 $$

In this problem. We need to find the re agents here. Right? So we need to know the mechanism as well. Right, So, we will just see here. This will be here. It will be. This is basically called. This is nothing good. This is R jones feared the agent jones Re agent. Yeah, this is oxidation reaction. Okay, okay, so now we can say that here we will. Right, here's like this, that here cr three. Aah bless. You can see and then he is am I? For my information, we have like this should there to eight. We can say this is. How did you get inside used here? Okay, so for the alcohol, we know that for that from alcohol, this card oxalic acid group is formed from jones free agent at this sierra three at this. Right then after that discard box, like I said, group we will to convert into Am I? That is this is my great. So for a married information, this structure is taken to form a AM I here. Okay, so now for the next one we can see here, that is all through here like this. So this is nothing but this is nuclear filic yeah, addition substitution, audition substitution. Okay, yeah. In this way, how the seal is taken like this, this this trick its electrons and this electron pair of wage that is alcohol will attack here in the Taiwan. Right, so this will take its electron with itself. Yeah. So this is nuclear clinic addition substitution reaction. So in this way here we can right here like this we can. Right, yes, yes. Mhm. So this is see it. Okay, so now for the third, when we can see here we need to remember some basic reactions like this, that yeah, this is all CS three kinds of things. Is it is just making So this is this, it seems like this seems like this is oh Friedel crafts the action. So in Friedel crafts reaction. This is a situation. Yeah, actually, so the uh from Benzene we will just put a generally as stress of fourth and it will become a noto. And remember this is a matter directing. Okay, so now we can stay here like this. Dad, this is this seal board is there. So this electron, one electron will take in here. Mm This this double bond. This is meta directing. So this will just the text is born because this is by one and this bond is taking this electron is taken by the electron negative. And when that is all mm After that this movie as it is meta directing and little group. So this will direct you like this. Thanks. So here we can right here simply. Right Yes, you can see it A 10 or three. It's two so four and this is seal. Yeah. This this this this oh ch three and this is N. C. Entry. Yeah jake. So in this way we can get this product is a product right now. For the last one we can see the mechanism. So this is this is basically we will just make it into double ones because we want or it as like this so we can just right here like this that this is possible to make from elegant to L. Came here we are using E to elimination. So this is a two elimination. Okay in here we can see this is the stable bone comes like this and this will this electron were taken by electro negative element that is beer. So here Q. It alcoholic is used right? So now this is hydro operation. It would undergo high cooperation to the action okay where bh trees used and we will use here like this and this double born breaks. And now this week protest to the here like this. So we will see H 20 Group and which minus we have taking a re agent and this makes and alcohol. So it is right here what are the the agents we have? You was here here it is key witch and garlic. Then this is Bh three okay. H two or two. And this is wait minutes basic medium you can say so this is a basic meeting. So this is how we solve this problem. I hope you understand the concept. Thank you for watching.

All right, so we're looking at graph transformations. So let's start off with a basic equation like y equals F of X. This is what we're starting with. So for part, a given why equals F four X. This is just one transformation they were looking at. So we have a four constant, which means it's either stretching or shrinking the function or the graph of the function. So in this case, since it's inside the parentheses with the ex, it's kind of a different situation. It basically does, um, kind of the opposite or the inverse. So if it was outside, the four was out here, it would be vertically stretching the function by a factor of four. So you kind of look at it like the opposite. Now, since it's inside with the ex, it's horizontally affecting it. Since it's a inside and rather than by a factor of four, it's gonna be by a backed by a factor of 1/4. So it's horizontally shrinking by a factor of 1/4. So essentially, it's the, um, opposite of. If it was on the outside, it kind of the inverse. So the part B were given, Why equals f of 1/4 x So consular thing Constant is on the inside, 1/4 of the princes with the X. So that means we know that it's horizontally this time, stretching once again. It's kind of like the inverse What's horizontal charging but a factor of four.

We have to find if the given transformation, um is 1 to 1, but not, um in order to find out the kind of cancer we have to use the road reduction that we know already and then looking at the rank and looking at the number off pivot columns pivot positions in each column. We can decide if it is wonder one or not. So let's start by, You know, we will keep the first. The role always fixed. Thank you. We will try to the malls on the streets here that understanding a screen. So if the first ro is fixed, I'm going to fix it at the same bad deuce. What? I'm going to change. But I am going to do the following task first. Odd to what will be my new second row? Well, it will be the previous second room. Added bit eight. Bye, five times album. Okay, so how How much will that be? Let's see. See, first IHS, we have to multiply eight by five with the entire first. True. So what will be it if I multiply by eight by five, this will become minus eight, right? This will remain zero This will become minus eight on this will become, um, four into eight by five. So it will be 32 boys. Thanks. Correct. So I'm showing it for one. And then I will expect that you would be able to follow for the the rest of the rules 100. So now our took That means what? Previously my art to first position was eight. So eight plus minus eight. How much we like it. We will get here. Cedo. Same way three plus zero. I'm sorry. It's not zero. Still, so 10 will then become If I write 10 over here, See, it will be 16th. Correct. I have a 16 over here. So my first well was 33 plus 16. It will give us 19. Then I have again minus eight plus minus four. So it will be minus 12 and then seven. Plus, Did you do by five? So seven less 32 divided by five. It will be 67 because 75 sir. 35 35 plus 32 is 67. So we get 60 seven. Bye. Fine, right. Same way now. The next action that I'm going to do is are three are three will be the older three. Plus are one is going to be changed. So whatever numerator off art that will come in the denominated divided very five. And whatever is the coefficient off are three that will go in there New Morita. So four by five, Hard one, Correct. So again, if I clean up the screen little bit I'm sorry. Then we will see what will be those numbers. And as I again say that for one particular But I'm showing all the steps I hope you would be able to figure out for the remaining glands. So now if I multiplied with four by five this number four by five I will change it to, uh, minus. I'm sorry when you take up minus for if I multiply this number with four by five, I will change it toe plus off eight. If I change this number, multiply this number with four by five I will change it to minus four and four by five. So 16 by fine Now what am I doing? I am adding this toe The previous told you so. Let us add element by element four plus minus four. It will yield zero again. Minus nine plus eight. It will yield minus one plus five minus four. It will yield plus one and then minus three plus 16 by five. So it will build one bite. Fine. Next the same way. If you see on four, he's going Toby at Fort plus the coefficient off. Three. Bye. Coefficient off first. So playing well, it one. So definitely the first term will be zero. The second term would be minus eight. The third term would be eight and the last time would be eight by five. Now, if you see these two rules 00 if you C minus one left, minus seat minus 11195 minus 88855 It's like there is an eight right throughout. So why can't we subtract the fourth rule from the first one after we multiplied the first one? Right? So let us try that. I am not writing the first two rows. Imagine There, there, in the third one, we will have this and my new four through will be our for prime, which will be eight times third row minus only for truth. So that will be zero my insider. Whatever multiply you get zero the eighth time for a third row. So it will minus it minus the next troop. So it will be zero. It will be zero. It will be zero. So now, at this point, if we take a look at the system, this is giving of a metrics that somehow looks like this minus five 10 minus 54 0 19 to a minus 12 67.5 zero 19 minus 12. 67 by five. Zero minus 115 I mean, one by five. Seattle minus one one one by five and then zero zero zero Syria. Now, what is so particular about it that it is the moment if it position food. Hello? Okay, look. Awesome, Trump. This means that this system off recreation have a free baby. This is means nontrivial solution on a dark to me. We dad? Mm, Yes, please. A little nice Mobile insulation. Mhm. It's more than one position means the consternation. P confirmation. Qin's the transformation t don't be. Come on, transformation. So that's a That's a visit

Hello. Everyone today will be disgusting. Multiple transformations on a function. So this is our, you know, function. Abou blacks equals X plus two altogether square. So just operable like this right now we have a new function. Apple bags equals X minus two altogether square plus five. So let's break this new pointing down, shall we? So how do we get from X Plus two two X minus two? Well, we can do so by subjecting quart from the original X was too right. And as you can see here because for is subtracted from every single X coordinate of the original function, this is what we call a horizontal concession. Keep in mind that all hallways on the translations actually inverse. So when we minus four here, we're actually moving our graph four units to the right, you see, So the blue crab ISS moved to the right for units away from the original function. And then we to simply at five to the new function. Right? So plus five years is added directly to the entire function. So this what we call a vertical transformation and it's very straightforward. You were actually just moving your graph five units upwards like this. So the black crab is actually moved five units upwards from the new function. The blue crab Really hope this helps Have a great day by


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