 First thing I wanted to mention this was pointed out to me this morning, and it's a very very subtle typo And it's actually from the original in the review that I gave you In the review that I gave you this one here On the very very last question I had a student and we couldn't figure out why our answer didn't match mr. Kamosi's answer key and Then we realized this graph itself has a typo just look up and you'll figure it out Just look up and you'll figure it out. Let me zoom in see this negative five right here Count how many squares down is it? And and so we were using this as negative four and doubling it to get to negative eight and I'm reflecting to deposit of eight ending up One up which was nine and off the page and we couldn't figure out why the answer key that is online mr. Kamosi made it he never makes mistakes unlike me. He's meticulous and perfect We couldn't figure out why our answer key wasn't matching his and then I went oh This is in the wrong place and I can't fix that that's from the original This was actually put up by the Ministry of Education So here's the plan I've given you all a little practice test those you are watching this at home You'll just have to pay attention what we talked about was we could either do a question-and-answer session But people said I had since I had a practice test from Alberta We could kind of blaze through that so we're gonna do that I will do about ten minutes of Q&A before your test not much more than that But when we start the test tomorrow, I'll do ten minutes of ask me a couple of questions That can be last-minute details if you say to me and mr. Do it I don't understand transformations. I'm just gonna move on somebody else Even if you say to me mr. Do it I don't understand reciprocal I'm gonna move somebody else if you say to me mr. Do it I was trying to do reciprocal with a twist and a reflection like what I was really nasty ones I kept getting the wrong answer that I'm willing to fine tune or touch up on Bear with me. Well, I have a beverage here So the little practice test is this one here, right and I think you should all have it's page in the book. It's page I don't know what page one apparently Find page one and a little book there Do not write a little booklet there and what I'm gonna do is some of these Will do just orally But the more tough the tougher ones I'll paste them into here and we'll do them step by step But I'm just gonna say to remind you please don't draw in the book, please Transformations So the test is done, I believe it's 12 multiple choice For some strange stupid reason and math 12 multiple choice tests the multiple choice questions on the provincial or with 1.5 marks each It's dumb, but since this is the last year math 12 is running I'm not gonna change my marks even though there's no provincial multiple choice is gonna be 1.5 marks each and Then there's the written section. Let me tell you about the written section You can either write this down or you can just remember it. I think there's seven questions Seven different graph. I give you the same like weird shape graph and I say do this do this do this I'll even tell you more specifically the first question is probably a slide up down the slide left right Very similar to the math mouse The second question probably has a stretch and a reflection third question probably has all six Vertical stretch or shrink horizontal stretch or shrink vertical reflection or not horizontal reflection or not left right slide up down slide Okay Somewhere in there you can anticipate alarm bell Right Gonna remember right though. You're gonna remember that by the way. I'm not doing this just cuz it's fun It is fun. I have to admit to see you guys jump But I did this started doing this about four years ago at the end of the year under the survey I had about 10 of my kids say I totally remember that stupid alarm bell thing so I was okay It's dumb, but it works and it's fun bonus You can expect an inverse how do I find an inverse? Switch the extra like to me as long as you're careful that one should be almost free marks But you know what for some reason the particular shape that I give Tempts kids to get stupid on that one the number of times I see half the shape go the wrong way because they relaxed They did all a tough part and now they're at the little tail bit and end bit of it. They're like, ah It drives me crazy You can expect straight absolute value That also to me should be almost free marks straight reciprocal and Then the last two questions there's going to be absolute value with a twist and reciprocal twist Reciprocal with a twist on your quiz. I gave you three things. I think on your quiz. I gave you a Reciprocal a stretch and a reflection. I'm not going to give you three things It's going to be reciprocal and one more thing either a slide up down or a slide left right or a flip or a Stretch but not more than one of those things which means you should be able to get there by hovering the whole way and keeping track of it By hovering your pencil. Oh invariant and now three up or Shooting off to infinity three up and still shooting off to infinity like whatever That's your task So very quickly Number one. What's the correct answer? Read the question to yourself first of all before blurting out an answer Read the question to yourself What's the answer? See okay, this is a classic multiple choice out of your 12 5 will be like this And what I mean is it's going to be straight glance at it think about it go to your answer You're not going to have to write anything down It may be more stuff than this To me a better multiple choice would be One left and three up and then I could have a one there a three there a one there a three there A one there a three I could mix and match a bit more and give you a few more choices, but do you understand what I mean by? It's a thinking question, but it's a straight recognition question. Okay Number two horizontally expanded and horizontally translated and Let's see that means followed by Well, let's see First of all Horizontally expanded by a factor of three halves this one. I think I'm gonna write down so this one. I'm going to go worry a clip now Horizontally in my mind. I almost always underline that because that just screams to me x x x x yes If we're expanded by a factor of three halves, what did I replace x with Amanda? Nice catch because it was always backwards So the first thing I would cross out here is what and please don't on your tests But the first thing that I would cross out here is what because I'm a good test writer Why would I even leave those there? In fact, probably I'd do this to really make sure they didn't distract me Then that would move it see you and it doesn't say a direction, but I think it implies positive so to the right What's the correct answer that one or that one? D because You would when you made the substitution bringing brackets This here is C right followed by horizontal expansion of three halves not the order that they gave me Okay, so that's a little tougher They threw some algebra in there too with that C units again We talked about how Trevor don't let that scare you is that box in your way or can you see okay? Don't let that scare you Easy way Ryan for me to take a basic question and ramp it up a notch is replace everything with letters In your head or on a scrap piece of paper in the margin replace it with nice happy numbers Do the math with the numbers and then say it's got to work the same way for the letters, right? absolutely number three So here is an example of one where you have to think a bit the graph is given below and Then it's transformed to that What's its new domain? I would consider this one a mini curve ball not a nasty curve ball, but a mini curve ball now Let's talk about curve balls on your 12 questions Two of them are one of them is fit is I would say very tricky One of them is medium tricky and one of them is all you're gonna kick yourself afterwards because I already know almost everyone It's gonna get it wrong and when I go through it all of you're gonna slap yourselves on the forehead because you want to pay attention tricky Okay, I call those all curve balls I will never give you a written question curve ball the written question. I've already told you what it is on the multiple choice section one two three at the most Okay, this to me would be a entry level curve balls. Let's copy this one You can always copy it onto a scrap piece of paper if you want to or you can just follow along By the way, I'll print this up this page right here up for you when we're done So if you learn better by writing down fine, if you learn better by just watching fine I'll print as many copies as we need whatever works best Okay, what's the domain right now? I don't know. What would the domain be if this was? 3 comma 5 what would the domain be right now? You see by the way Ryan see what I did they gave me letters. I'll fall back on nice familiar numbers I'll do the math for that's gotta work for the letters If I told you that was 3 comma 5 and I said what's the domain of that graph? What would you say? I'll give you a hint x x everything to the right of 3 is that not correct? Domain right x greater than or touching 3 Yes Yes, yes, yes, I can't I'm not getting any feedback from you. Yes. Give me a nod if I say yes I'll make it then I know okay. Is that okay Steph? I guess that's the domain Okay, I saw my way through that didn't scare me ain't so bad Now let's walk through the transformations Anything horizontal will affect the domain Anything vertical, I'm not even gonna care about because how can that possibly affect the domain? First of all first of all alarm bell. I don't like the way this is written This should be written as it should be that yes What's that mean horizontal or vertical? Okay, I better take care of it then because it could affect the domain expansion by two or compression by a half which one Thank you Horizontal compression by a half What's this mean? What letter is that right there? Nicole horizontal compression by a half compression by a half I was going to the next step three Right, I think that's what you would do if it was a number wouldn't it like if that was a six It would become a three and then three right or if that was an eight it become a four and then three right It's a P. You divide it by two and three It's that one Remember these days Never again The last year's run Memories I don't know. I haven't even looked at the pre-calc 12th curriculum to be honest That's that after spring break sometimes then I'll care Yeah Is that okay? That's an example of how I would handle a curve wall now pause Did I do anything new there? Nope stubborn and clever Okay, and strategy number one they try and throw something algebraic at me put numbers in there Shut up put numbers in there do it to the numbers. It's got to work the same letters That you give a question. Are you looking for funnel or if someone here was we're good. Okay, let's go to the next one The graph of that is a reflection of the original in what line What kind of reflection is that horizontal or vertical? It's my favorite horizontal What line am I spinning about though when I do this? Which one is a horizontal reflection a reflection about the x-axis or about the y-axis About the y-axis Okay, a vertical reflection is about the x-axis. Do I say everything's backward yet? What about C which which transformation is a reflection about the line y equals x there is one Amanda inverse What about D they had to come up with something I Yeah, we ever brought in y goes negative it to me I'll use the words if you understand the way I mean to me D would be a stupid guess You've never seen it before it's never sure why would you circle that one? Right, I mean at least I'm gonna circle stuff. I'll circle things that I've seen before you. It's never mentioned negative x Turn the page or do you guys need to next page over? Oh turn the page. Thank you for following along How does that compare? With that how does the that graph compare with y equals x squared? So now they're saying we've given you some function notation. Here's a specific graph Here's the parabola and I'll be honest look up. I Would do this first for multiple choice because what is that to what? To left I would cross out C and D right now even though that's not the correct order to graph it in if I was answering this I know I Assuming all of you will get that part right because that's math 11 still I would say that's to left I would cross out C and D Expansion by four compression by a quarter which one? expansion by four a Okay, so there's an example of a more advanced knowledge question, but still a knowledge question Did we really write anything down? I probably would on a test write some things down because you're always hedging your bets But you know certainly if you held the gun to man, I could do that man. No problem number six Now this is heavily graphics intensive I won't give you one like number six on your test because I'm not that good at graphics I would probably find a way to phrase this into function notation However, here's what it says this graph is transformed four ways to produce graph one two three and four Which of the following corresponds to the transformed graphs? Let's see. How does this and this relate? Huh? Inverse, how could you get that or figure that out? Here's what I did. I said that looks around negative three negative two ish That looks around negative two negative three ish I think I switched the x and the y around and yeah, it's also a reflection about the line y equals x What about here that one? right See graph three reciprocal Let's see. Oh, yeah, two asymptotes right there one high one high standard negative one high standard Yeah, I'll give you reciprocal and and D Horizontal reflection I doubt I'd give you all four of these in one the odds are I'd give you just one graph and say tell me What's going on? Well, actually the odds are I won't give you very many I did the graph on the written and that took me about two hours of typing The graphics are a pain. I wasn't gonna do it on the multiple choice so far so good number seven That is shown below Looks like the absolute value graph which are the following is a graph of that That's interesting because we're taking the absolute value of the absolute value, but don't let that freak you out Just think v-shape I see two things going on here absolute value. Yes, and two Down which is first Two down so in your head Move this graph two down And then take the absolute value. What would that look like? Sesame Street is brought to you today by the letter w and Now you know the graph for a w by the way question the coal Eric No, we're good. Okay Number eight the partial graphs of two functions are given below There's f of x the original There's g of x the new one and I notice look look look they gave me a point Zero common negative two became zero comma negative a half What do you think's going on here looking at the graph and looking how that point was effective? I think reciprocal right a negative two became a negative a half. I think they just flipped it Let's see here. We're getting bigger. What are we doing here getting closer to zero? Yeah, I think this is reciprocal. I think G of x is the reciprocal of the original. Is that okay? I'll lose you Don't lose you. Good. Okay. I'm learning to read your guys body language Yes, I don't know. I'm having a tough time reading my classes this year So do you notice that the negative two became a negative a half that suggested to me that it was reciprocal, okay? Getting further from zero getting closer to zero Getting further from zero getting closer to zero. I think this is reciprocal. I think g is the reciprocal of the original graph The answer is D Is that okay? By the way, I would have photocopied an email this out to you guys, but what does it say in huge letters right? I don't have the rights to this otherwise. This is a nice little practice test, but sorry Okay, here's a nice little twist number nine fact this one's worth flipping so This is how I can take a basic question and turn it from a C to a C plus or a B minus Emily, what's that mean for? What's that mean for left and one which one? Sorry, I caught you off guard my bad Amanda, what's this mean for? And and I'm sorry, but I was gonna say and I would expect every one of my students to be able to get that in their sleep But maybe you were sleep right four left and one down that to me would be too easy So here is sorry that I said there's gonna be like five easy no brain That would be one of the five easy no-brainers, but how could I make this question a bit tougher? Still four left and one down, but give you a graph and say what's the new range? Well, what's my old range right now? What's my range? What's the range of this right now? Come on boys and girls. It's math 10 and math 11 Steph, what's the range right now? One is a number one is not a range How high does this graph go? How low does this graph go? How will I write that first of all with a range letter Y? Yes Everything below and touching one Yes You need to know that for tomorrow And you know how to write a range tomorrow now How has this been moved Emily for what? one what With authority will a left effect a Y So I'm gonna ignore that will a down effect a Y Yeah, move the range one down There's your new range easy if you think about it the right way Impossible if you've forgotten how to do the range or you just don't you like you know what most kids when they come across Something new they panic and they freak out again. Did I do anything new there? No, you guys doing okay back there? Okay, I figured so sound like you guys are working ahead make sure again. You're not writing on my tests. Thank you number 10 Again, here's another way that I can take a basic concept and just add a bit of a twist to it Which of those transformations would affect both the domain and the range? What affects the domain Horizontals, right? What affects the range? Vertical so better have both if it's gonna affect both Does that have both? Nope, does that have both? Nope, does that have both? How do I find an inverse? Which means I think your domain would become your range and your range would become your domain and that would definitely absolutely deep These I would argue are among the toughest multiple choice questions where they give you one graph and say find the equation So I'm gonna copy this one and I'll show you how I would approach it. You guys doing okay? I don't care if you're not you're still stuck. Well, no you can go whatever you want to it's not a detention All right, they want the equation of this well Which way is this long skinny thing pointing right now originally upwards? Which way is it pointing when we're done? So I would definitely make a little note to myself There's a vertical reflection yes That helps me. You know why that's wrong and that's wrong. Why are A and B wrong? No vertical this is why I've been trying to get you guys to glance at your answers every time you do something Because now even if I freeze I got a 50-50 change in fact if I can do that for every question knowing nothing else I'll pass the test because I got everything 50-50 right in theory. I'll pass the test we'll learn improbability That's not quite as easy as you think Has it been flipped left right at all? Nope, so if any of these had a negative in front of the X I would ignore that but none of them do What's right here Trevor? Right in front of it What's right here? Right in front of it also a you know what I guess a vertical stretch by a fact. I'll write it down vertical stretch a Vertical expansion I think sorry is the phrase we use vertical expansion by two but truthfully I don't care too much because that's apparently the same in both answers What I really need to figure out now has it been moved to left or To up I think this is the point that I'm interested in following How far left right is it right now? Three to left negative three I'm pretty sure it's this point. Yes, how far left right is it right now? Still negative three. There's no way it was to left you'll notice. I didn't find the equation. I Got rid of all the wrong answers. I Find that's easier than trying to come up with the equation. I only find the equation as a last resort That's how I do that one. Oh, I guess I should write down To up since when I print this up you'll freak out if that's not there Maybe you won't okay The given quadratic function this parabola has a positive X intercept right there a Negative X intercept. Yep, and a negative Y intercept. Yep Which of the following are true? The what's this stupid symbol mean? The inverse will have a positive Y intercept a negative Y intercept and a negative X intercept or Statement to That there both neither one or two. Let's analyze them one at a time. How do I find an inverse? Too slow. How do I find an inverse? You know what if you could write on this what I would do is I would cross out that X and you know what letter I would put there a Y and I would cross out that X and you know what letter I'd put there Keep me going people and I would cross out this Y and you know letter I'd put there and I think positive Y negative Y Negative X I think statement one is true on an inverse Because you when you switch the X and Y around that's the actual statement that you get statement one is true And I think statement two is false if it has no X intercepts. Oh the reciprocal I'm sorry the reciprocal will have no X intercepts and a positive Y intercept. I thought this was inverse I read too fast. Let's look at what would the reciprocal look like. Well, there would be vertical asymptotes right there and right there So there would be no X intercepts anywhere zero high would become an asymptote So this first line is true. What about the Y intercept? How high am I right there roughly? Negative two what would the reciprocal of negative to be? negative a half still negative Will your Y intercept become positive under a reciprocal transformation? That's wrong. The answer here is statement one only the answer here is C I'm not gonna give you one of those mix and match questions on your test By the way, your test is similar to the provincials if you want to know what the multiple choice will look like the review package That I gave you guys a month ago is what the multiple choice will look like But this has got some nice thinking questions and it let gets you used to writing a test Turn the page What's the equation that represents the inverse of that? How do I find an inverse? Switch the X and Y. Thank you. That was much faster. So I would start out by going X equals negative two bracket Y minus six all squared plus three I glance at my answers. Oh, it looks like they got the Y by itself Sometimes they'll let you stop right there. I've seen it once in a while We're all they wanted to do all they wanted to test was do you know switch the X and Y around here I think that's they want me to get the X by itself how to get the X by itself Yeah, yeah, I would do this absolutely keep going Okay Now when I divide by negative two Look at your answers. Is there a negative two in the bottom of any of your answers? Just a plain old to you know, I think they did I think they took this negative and they moved it to there to the top There's a negative kicking around. Oh, and you know what that would make this X? Negative and you know what that's going to make this three Positive and that means I'm crossing out that one in that one. You see that little line of reasoning. I Noticed I told you glance at your answers every time you do a step as soon as I divided by negative two I glance you know, wait a minute. There's no negative twos and then I said Oh, I noticed that some of these are positive and some ah, they took that negative and they moved it to the top Ryan And they distributed it. I figured that out. So I'm gonna have this right now three minus X over two equals Y minus six all squared No Right How do you're a squared Ryan? And when I square root what had I better remember and there's a bit of a hint right there When I square root, what do I have to remember? Plus or minus so they must have done this they must have gone get rid of the squared plus or minus Square root how would I get the Y by itself? Amanda Plus six. What's the correct answer then? Oh, is the plus six inside the square root or outside the square root? Outside correct answer here. Absolutely is a because you plus six afterwards. I am going to ask you to find an inverse equation. I Am going to ask you to find an inverse equation on your test But not this one. I think it's multiple choice Remember the big transformation unit review quiz this big boy here remember this I Love this question. I love this question. I love this question I really really really really really really really really really really really really you know what? Question number six. Will you marry me? There's your hand Okay, there's your hand. I'm not repeating myself. I expect you to pay attention Okay Or you can rewatch the video and listen to my verbal instructions. You're at a tutorial. I'm not repeating myself. Get up not a chance I'm giving it my free time. Okay That means you can expect to see one that has X's on the top and on the bottom and You'll have to remember to cross multiply and Oh, we had more than one Y. We got them to the same side How did we what was the grade nine mathematical operation that we're able to pull out of our back? GCF I'll let you think about that or you can rewatch the answer key or you can phone a friend But I like that question Eric we're back Were you ever here? Okay Here's an advanced reciprocal multiple choice question Says an invariant point is a point that remains unchanged We're I've made you guys memorize that term because I won't tell you that definition I'll just say in variant points. You know what it means Use the graph of that to determine the number of asymptotes and the number of invariant points for the What transformation is one over G of X? Reciprocal oh Word asymptotes come from on a reciprocal wherever the original graph was what? X intersets one Two Three how many asymptotes three I would cross out a and b right? How many invariant points invariant points are where? One yes two three four There would be five invariant points Well, what did I say three asymptotes or two three asymptotes and five D? I believe is the correct answer again Because asking you a reciprocal question on multiple choice is pretty tough because you're really it's drawing But here's some of the stuff they could throw at you or they could say What would the new domain or the new range be actually probably wouldn't but whatever that's my hand in the corner. Yes That's fine This is not an attention. I'll post this online. I will check your oh Joel Check your email tonight because by about 7 p.m. Tonight I will send you the video link to this tutorial and I will send you this file as a PDF But you guys that are here. I'll print up this file for you when we're done as well Okay, too far Computer's getting old number 15. What's going on number 15? Which transformation is this? How do you keep how can you tell it's inverse? Yeah, this is my preferred notation. I like this better so The new one is gonna go through Four zero is gonna become oh, you know, I think your inverse graph I think is gonna still go through four zero and zero four. Let's pick a better point. How about One two three well, which of those is the inverse just glance down and tell me See is and you'll notice this whole line actually stayed invariant sort of it didn't quite but it repeated itself. Okay Definitely gonna be something like 16 or 17 or 18 where I give you a point And then I give you something in function notation and say tell me the new coordinates So this is worth clipping I think mr. Do it and the way I told you that I do this is I Write the point over to the right negative 12 comma six. I list what's going on. What's going on here in the correct order Steph I'll pick on you because you look like you're awake. Tell me the transformations list them What's the first thing you see here in the correct order, please? So don't yeah Vertical I always want that word for vertical horizontal vertical expansion by two She right? Why is it a compression? Okay, by the way, can I guarantee that on the multiple choice test? I will have that answer to pick from yes, okay In other words that by far the most common mistake right there And I'm glad you did it during this to a tutorial because it's gonna refer refresh our memory not to do that But the bad news is in my answer key on the multiple choice You will find that answer if you expand by two it'll be there so vert Compression by a half keep going okay Vertical compression by a half that's going to become a three vertical reflection. That's going to become a negative three For right if you're at negative 12 and you move for right you end up at negative 16 or negative 8 I'm willing to bet both answers are there. Oh, yeah, they are negative 8 Okay, so this one here correct answer B We're still starting with negative 12 Comment six those you need to go no problem Check your emails. I'll get it out by Hopefully by seven in the box, please It's stacked the same way as the other ones would really help. Thank you All right You a can I'm you good you wait actually you know, let's go to the back corner Joel What's going on here? Can you list them in the correct order, please? I disagree with you? I do I Do see an expansion compression I Need I Again again again the first word I want to hear every time is horizontal or vertical folks By the way, are you not figuring out? Why because as soon as you say horizontal we can cross off certain wrong answers often, right? So I'm doing you a favor horizontal Joel, what'd you say? I Agree always folks keep going. Yep. I agree So horizontal compression by a third that makes it negative four Horizontal reflection that makes it positive four eight down that makes it negative two There it is It's very systematic Maria if you do it list point move out 18 would be a minus level questions. Let's handle here's reciprocal with a twist for a single point Again, the point was negative 12 comma six There's two things going on here Alex I see reciprocal see it and I see six up Is it six up first and then reciprocal or is it reciprocal first and then six up? Yeah, if I wanted you to do six up first, I would have written it this way I would have put the plus six inside the reciprocal six up Then reciprocal everything. That's not what this says so Ready Alex reciprocal six up add six to that glance at your answers, please What is the correct answer if you add six to one six? Yeah, six in a six they just wrote it as a mixed numeral, right, which was easier than an improper fraction Seeing why I'm telling you to glance at your answers all the time by the way. Oh, we're learning Book you're dropping on the ground or you saw to go okay in the box nice and please. Thank you so much Absolute value with a twist so absolute value and Then vertical expansion by two. Yes So absolute value of six is going to be Vertical expansion by two it's gonna become up It's gonna be negative 12 comma positive 12 negative 12 comma positive a Right there. Okay Every once in a while, I don't think I did this on your test, but might be on your final I can't remember they'll give you a specific order to do things in so it says Find the image of point a if it's reflected in the line y equals x. What's that one? Dominique switch the x and y around so instead of negative 12 comma six six comma negative 12 and now horizontally expand and Now move one left in the order that they told me for some reason. Okay, we can get there written section. Okay I'm not gonna give you one like this. I'm gonna pass I've told you I'm gonna give you one something like this on your multiple choice where there's x's on the top and on the bottom And I say find the inverse. Would you like me to do 22 be with you? Yes, I'd be happy to Is Eric aware of what I'm doing? I wonder so the instructions said find the inverse Eric, how do you find an inverse? Without a pause for some mystical reason. I'm gonna ask you again. Say it again without a sudden strange little pause in your answer. How do I find an inverse? So I think the first thing that I would do if they wanted me to find the inverse of this yucky looking fraction Eric As I would say six y minus one over four y equals x you're good with that What don't I like about this? Really? What don't you guys like about well to find an inverse? What do you usually do afterwards? What do you get by itself to finish off an inverse? What don't I like about this? I got several y's fraction. You know what I'm gonna do here Eric I'm gonna do math eight What is math eight? Sorry Trevor okay now Eric I'm gonna do this once and once only I won't do this for the rest of the year because I find this offensive in math 12 I'm gonna pretend from now on you'll always see that any number is a fraction It's always over an invisible one because this is one fraction equals one fraction cross multiply and Eric when I do that I'll get four x y equals and one times six y minus one is just six y minus one We're trying to get the y by itself Eric. How many y's are there in this question? Let's get them to the same side How could I move this guy over now? By the way, let me pause So this is where I see kids start going stupid on me weird on me. They'll divide by why no No, you've got you don't want to bring fractions back At the very end you'll have fractions, but right now you've got the y all on ground level Yeah, I'm gonna minus six y from both sides and Eric when I do that. I'll get four x y minus six y equals negative one Eric how many y's do I have right now? How many would I prefer? It would be wonderful if there was some kind of a grade nine mathematical operation We use math eight to cross multiply It would be wonderful to the grade nine mathematical operation that I could put on my back pocket That would somehow turn this from a pair of y's into a single y What was it Brianne now mean taste Eric and say it Greatest comment factor. I know I'm making fun of you because you weren't paying attention ten minutes ago get used to it Factor out a y Eric and I get this Now the y is easy to get by itself because what's happening between the y and the bracket mathematically Eric Adding subtracting multiplying or dividing so how will I move the bracket over? Now if this was a multiple choice question There is a chance With that little negative sitting here There is a chance that maybe Brianne when you did your cross multiply thing You did this first and you had the six y minus one on this side and The four x y on this side and so you moved all your stuff to opposite sides Your answer might be the complete opposite of my answer These two are the same thing where the one is positive negative The four x is positive here. It's negative the six is negative here. It's positive. Those are identical answers So if you don't see your answer, don't freak out fine gets complete opposite with everything opposite, and then you're good Let's practice. Yeah Then you'd have a two y by itself, and then you have to divide by two afterwards You know what when I say GCF I should say CF factor out the y okay I'm Good to guess that and correct me if I'm wrong you folks are okay on basic transformations So I'm going to spend the remaining time looking at reciprocal and then absolute value with a twist reciprocal with a twist and Everything's with like I have six things that sound good so Number 23 says the sketch of this graph is given below. I'll cut and paste it here Unfortunately here. You won't be able to draw with me. You'll just have to follow along best practice is to draw it, but such as life Thanks for closing the door It's the hat. It's a Carolina hat. I'm okay with that. By the way, what's this one here? What how do I find an inverse? You guys are okay with that one just do it really careful, but literally switch the X and Ys around on the graph Okay, and I folks since you're the last one staying here. Listen to me every year on this test I'm going to ask you and I'll even be more specific I think it's the third or fourth graph that I asked you to do it's an inverse Every year kids get all the tough part of the graph right and it's the final section That's the easiest and for some reason their brain shuts off and they trip on their brain They have a brain cramp. So just be a little paranoid on the inverse be really really really careful. Okay Let's do risk for me I all of a sudden they start going off in the wrong direction because they think they spotted a pattern and that pattern isn't there and They just keep going they give it a tail. It's not there I don't know like it This is one and it's now been four or five years in a row And I don't know whether it's this specific graph that I'm giving you guys or it'd be an interesting I could do like a you know double blind study or something, but it's just I've just noticed so there's my warning Instead, let's do this. Let's do reciprocals. So let's do Okay, and I'll do it right on top of this graph. I'll do it In red doesn't really print for you guys, but it'll be a lighter color. You should be able to spot it What's the first thing that I do to find an inverse Sorry find a reciprocal Dominic More specific. Okay. So I'm gonna write down here Asim X intercepts can be an asymptote there Can be an asymptote there this question. We were three marks. You just got a one And I'm gonna argue that's close to three marks really What's the second thing I look for Dominic? What are the invariance invariant Invariant. Oh notice it stops here continues here. I'll be careful with my arrows. Oh And this whole line is going to be invariant. Yes Now what bug Standing here Standing here Shannon as I move to the left is my graph getting further from zero or closer to zero So it's gonna shoot closer to zero kind of like that arrow on the end arrow on the end as I move to the right getting closer to zero. What's the reciprocal gonna do? You say shoot off to infinity if you didn't just say you didn't say it loudly Right Down here this whole thing would be invariant This here. Oh Getting closer to zero but negative shoot off to infinity but negative Right. No. Yes. No. Yes No, yeah. Yeah, we're good. I don't mind you guys are here You guys are freaking out because I drew my asymptote in the wrong place I Caught it though. It's the other nice thing if you're stupid like me. This will catch your mistake that better Because this is curving closer to zero but negative shoot off to infinity but negative Closer to zero but positive shoot off to infinity but positive now this one here it comes to a stop Alex How high right there? So if I was marking this I would look for a big dot at about one half and Definitely a dot stopping if you put an arrow on there, I'd have to slap you for a half mark Now I said to you I'm gonna give you a straight reciprocal on your test and I won't botch it To the other so it's right and I'll give you a reciprocal with a twist So what kind of a reciprocal with a twist what I do? I'll copy the same question the same graph. Oh You get back to the original right there What if I did this? Flip everything, but if you're doing it from cold turkey, I would say Well flipping it will that change your vertical asymptotes? No, so maybe this time mr. Do it can get them correct Did I get them right this time? Oh? Oh Sorry for those you watching at home for your 30 seconds of sheer panic when you're wondering what they had done in variant points One high oh, but then reflect negative one high in Variant points one high. Oh, but then reflect Negative one high in variant line negative one high reflect Positive one high Now I would probably put a little x right there and a little x right there Little x there and a little x there because those are my original invariant points And that's where I'm gonna go back and do my bug trick from now. I Wouldn't put a dot there because you put a dot you're telling me it's part of your answer But x's I clue in those are little placeholders so right here as I move to the left I'm getting bigger so as I move to the left it would get closer to zero, but positive reflect Closer to zero, but negative Shoot off to infinity, but positive reflect Shoot off to infinity, but negative Right shoot off to infinity, but negative reflect shoot off to up my pen sleep Shoot off to infinity, but positive shoot off to infinity, but negative reflect shoot off to infinity the positive, shoot off to infinity but positive, shoot off to infinity but negative, and it would stop at negative a half. Let's do one more reciprocal with a twist, and then I'll do a couple of absolute values with a twist. You can go whenever you need to. Okay, how about this? You know what, let's write it this way. No problem. Oh, this would be a vertical stretch by a factor of four after reciprocal. Here we go. Is the vertical stretch going to change your asymptotes? I don't think so, so maybe Mr. Dewitt can get those correct again. Invariant points, they're going to move, so I'm going to go little x there, little x there, a little x at the beginning and the end of this invariant line. How high are we right here, Alex? Reciprocal, still one. Vertical stretch by a factor of four. Oh, okay, a little weird, but okay. How about right here? Oh, you know what, that would also end up four high. How about this invariant line? Well, it's negative one, reciprocal, still negative one. Vertical expansion by four, one, two, three. You know what, I would look for that right there. Can you hold that thought? Because this one isn't. See? How high is this point right here? Take the reciprocal. What's four times a half? I'm going to expect you to handle basic fractions like a half and be able to, or you could go to Calculate if you need to. Anyhow, that guy ends up strangely enough being invariant right back where he started from. In fact, I think it would do this. Closer to zero, shoot off to infinity. Multiply that with a vertical expansion by four. Really shoot off to infinity quickly. Getting further from zero, closer to zero. I think it would do that. I think, I think, I think, I think. No problem. Hey, what about this section right here? It would shoot off to infinity, but with a vertical stretch, it would really shoot off to infinity. And I guess technically this point right here, if I take the reciprocal of a half high that's too high times by four, you could make an argument that I should be eight high right here. I don't think Maria I would be that accurate. Wouldn't worry about it. Here shoots off to infinity. Really shoots off to infinity. What am I missing? Here shoots off to infinity. Here gets closer to zero. Is that okay? By the way, the reciprocal of the twist, it's the last question on the test. It's the last question for a reason. I'm expecting some of my kids to get it wrong. It's the separate the A's from the B's from the C pluses. But you'll notice, I think I said to you, I'm not going to give you a reciprocal with two twists, only with one thing. Either a stretch or a reflection or an up-down slide, an up-down slide, you just move everything up at the very, very end or move everything down at the very, very end. A left-right slide with your asymptotes and things around. But that you would get by counting. Those I haven't done, but those aren't too bad. Now, since you guys are packing up, are there any specific things you would like me to go over? Otherwise, I'll print this up for you. But were there any specific questions you had where you're going, nah, I'm not so sure about whatever. That was your first, not a hand up. Okay. We're good. We're good. We're good. Alex, we're good. Carol, we're good. Yeah. That was, okay. I don't mind sticking around if you want to. But since they're packing up, I'm going to pause the video here. How many of you guys would like to print out of this little thing here? One, two, three, four, five. Okay, first of all, let me pause the video.