[Music] get ready to the countdown tuber Malaysia inititive Malaysia Guru [Music] Malaysia okay assalamu alaikum and hi everyone teachers parents and all the wonderful pupils welcome to Academy YouTuber how are you doing today I hope all of you are ready for today's lesson before we proceed let's begin our session with umul kitab Al faat and for the non-muslim you can pray according to to your religion bman okay let me introduce myself to those who don't know me I am Madame Aisha blue and today I am the moderator of the day as everyone knows the school are now closed due to MC cmco how do you feel but don't worry teachers of Academy YouTuber can help you to prepare for your stpm our mathematics T stpm will be on uh our mathematic T stpm class will be on Saturday okay like this like today 4 pm every week okay so please set reminder and fill in the timetable that you can get from Ed Malaysia telegram group all right let me introduce our teacher for today's lesson we have Miss Li yet or known as teacher IM in the house okay so uh that is our teacher today okay we are now live from missim y im's Channel and do support her Channel as she has lots of mathematic te videos for scpm in it today we are going to learn functions gr make sure sure to follow the class until the end and not to forget we do have culing okay culing where are you culing okay Che Zana okay cheu Rizal and also Mr shahon to Ure the smoothness of the class okay so before we begin I have a few reminders to all of you first pay attention to our lesson stop chatting and you the chat session wisely number two please pay attention to our uh please pay attention uh no sorry regarding the certificate link okay regarding the certificate link the link will be given at the end of our session so make sure to follow the lesson until the end and the link will only be active within 30 minutes okay please please and please is to fill up the forms correctly and within the time limit okay and the password for the certificate for today's uh lesson is Lio l i m a u Lio okay and for those who don't have the Ed the email please apply because we will uh be using the Ed email soon okay we will invite um you to be on stage but make sure you are ready with your camera and microphone on okay and mute your YouTube while you are on the stage so without further Ado let's welcome teacher IM okay the floor is you okay thank you madam blue hi I'm teacher IM I make videos to help my students score better in STV MSD paper well I hope my videos can be helpful for you too yeah that's my tagline all right now I have here uh we are going to talk about functions today but before we go on I would like to show you something okay let's go to the slide Ling thank you now if you look at the slides here I have other math teacher right I have other math teacher who will be coming over soon last week you saw uh teacher een in with me in the studio and then today you have Che Guana she's there just now you already she is already already hi high and by uh not by hi we say hello to you all so those are my these are my teammate actually I have two more admat teacher okay but they are not here yet so I didn't introduce them yet so I have two uh teacher e is teaching mathematic T and teacher Zana is teaching mathematic M so maatic M students go and tell your friend uh those are taking mathematic M go and tell them I have I think of you too I think of the students who are taking maatic m too all right so now let's say if only you all are having class how about your brothers and your sisters well no worries here I have all there are other subjects okay and we have other subjects uh of for stbm we have Aila foran there our Madame Aisha The Madam blue just now she is teaching m and then we have just now you saw him he's teaching and we have two more hereu how andu Yi they are teaching uh accounts okay so I think this is uh about all we have for stbm uh I believe they just found a sunny visual teacher for sdpm to you can tell your friends to stay tuned and for your brothers and sisters there are lot lots of more okay so we we have like so many so many teachers in the in Academy YouTuber okay uh we which will give you okay just now you saw uh the beautiful te ging okay she's the math teacher in and teaching mathematic okay and then anybody else here oh okay they are not uh with me today but sometimes they will be with me but so that's my beautiful miss Ling and then you can find the timetable for your class in www Academy we I will be talking about uh oops let me I will be talking about functions now functions in form six is kind of different from functions in form five in form five when you learn functions you basically just learn function but in form six functions are separated into four parts okay you have uh functions you have exponential and logarithmic functions you have Trio favorite right your I know your favorite is trigonometry favorite and then we have the polom and rational functions okay so in functions itself you have four different things we will try to cover for you don't worry okay if you don't understand anything just leave comment in the chat box we will try to help you okay last week last week somebody left a comment and today's lesson is based on that few person I think I counted like six person who asked for it so I made this video for them okay so you can leave your message uh leave your the words in the chat box okay and then tell me what you need we will try to make it for you okay we will try we cannot Pro promise 100% but at least if we don't make it in the uh class tambahan okay we don't make it in the class the pre tuition class we will also make them in our Channel okay so so subscribe right next one is well as you know today I'm going to talk about function so function got four subtopic inside there we will cover one by one so the functions as for functions we will have inverse function composite function very familiar okay you learn that in your form five inverse function and composite function then you have the uh once you learn when you are doing inverse function your teacher will have told you during uh doing when you are doing inverse function you have to check uh one to one okay you have to check about one to one and then uh when you are doing composite functions there will be range and domain involved okay and the big thing inside function this chapter is sketching of graph why do I say so because from 2013 until 2019 basically most of the question comes out uh involving this uh sketching of graph okay the thck that you see the ticks that you see around here uh around this beautiful flower I don't know why is my my my earphone disturbing I'm not digging my ear okay baby I am like this is disturbing me see the earphone it's trying to fall off okay so now uh what you have here the the double tick means it came out twice okay the double tick means it actually came out twice [Music] or not if the function is one to one or not okay so most of the time when you look at the question it doesn't like it's not like from five question from five question when you look at it I say okay I'm doing inverse I only do inverse but in form six they mix and they match okay if they are talking about functions they could be asking for inverse and at the same time they ask for composite they might ask for composite and then they will ask you what is the uh inverse of the composite so it will go back and forth or when they ask for the composite they might ask you what is the range or the domain of the composite okay and maybe after you do the composite they will ask you if you can sketch a graph for that composite function okay so you have to understand it is a tal uh thing you cannot like study okay I love composite I only do composite I don't need to study inverse what if like I say it comes composite and inverse then you will miss your marks already okay so you have to understand in form six they mix and match the question so I give you a tri triple tick is that a question somebody trying to say something no no okay no no no okay thank you so uh this triple tick is actually uh problematic for lots of student because most of the time students have no idea what and how to sketch the graph okay because most of the question in a function not I would say it is easier for example when you want to find range or domain it also use sketching of graph when you want to find whether the graph is a onetoone function or not it also use scatches teacher okay there is a a request actually from teacher please give us tips for sketching the gra tips for sketching the gra yes baby I'm doing it today I'm doing it today this is what I I put a triple tick on my on my uh work today because I am going to teach you from Step One until you are able to sketch the graph but I'm going to concentrate on basic graph first if you want to see the uh logarithm graph exponent graph trigonometric graph well you know the drill you have to go to my channel well because I I only have one hour I couldn't cover everything here okay it's not that I don't want to it's I couldn't okay I need the time okay today I'm going to concentrate on sketching the graph and then teach you how to find the domain and range and at the same time I will talk about the one to one function okay to check whether the function is one to one for composite and inverse function you studed that in form five before it is actually the same okay it is actually the same so I don't want to cover that so today I will cover from sketching of graph to one to one sketching of graph finding domain and range let's get to it now we want to do sketching of graph so we have to know some basic graph okay so this is a straight line okay this is called the identity function this identity function is actually y = to X or FX = to X okay so what are you what will happen if I want the domain and the range of this graph well let me uh let me okay domain means is on the xaxis we will be seeing anything from the xaxis on the anything on the xaxis okay so I draw that so that I know that is the x-axis and range will talk about anything on the Y axis so I will talk about whatever on the y axis so if you look at this uh function graph you will notice that on the xaxis you will the domain covers the whole thing so the domain covers from there to over that side and covers from here to over that side so the domain of this graph you can write it as from from negative Infinity to positive Infinity okay why do I use a round uh bracket for that well you I use a round bracket for that because there is no limit to that Infinity it is until the end and until the end okay so there's no limit for it so I use a round bracket so sometimes you say teacher teacher can I the question for set how can I write the answer in set notation so if let's see if your the question ask for set notation well this is the set will look like this X and then you have a colon sometimes inside the textbook H sometimes inside the textbook you will see a straight line here okay or inside revision book okay then you will say that X is the element of the element of of real numbers why real numbers because it it covers the whole thing so you will might ask me teacher should I write this answer or this answer actually if the question did not mention in set notation you can use both you can write your answer in both but if the question asks you whether uh in set notation then you use the set method okay but I always tell the students this type the notation method is much better much better because it's harder to make mistake okay now talk about the range okay let me talk about the range so let's see let me talk about the range so the range for example if I take the range here m i take the blue color Okay so let's say if I'm I want to talk about the range so this is the position of the range from there to there so again it is involving the whole length of the y axis so if it involves the whole length of the y axis so the range is going to be from negative Infinity to positive Infinity okay so if I want the negative of the graph I use back the same color I don't want to change color so so this will give me this line here H can I get a straight line yeah okay I got a straight line well so that is that straight line there so that is the negative X okay so I will have my Negative X over there and I will get uh negative means it will reflect okay if you have a negative X so it reflect on the y axis so when I want the domain if I want the domain is going to be also from negative Infinity to positive infinity and if I want the range again it will involve the whole thing here on the y axis so again it will become from negative Infinity to positive Infinity rounded okay so this is the first graph that you need to know now for the second graph that you need to know this one you have to be very careful okay because this is a squaring function a squaring function involve what a squaring function involve minimum or a maximum point so how to see whether it's a minimum or a maximum Point well the minimum point or maximum point will involve whatever you have in front here okay whatever ever you have in front here if this is a positive for example if this is a a then if you get like two for the a uh then it is a positive number you get a Smalling graph if it is a negative value you get a set graph okay so for this case if I have a sming graph here the original basic graph you have a sming graph here so for negative you should be getting a set graph let me draw the set graph okay it's very easy to remember well if your a if you get uh for example is your maths you get more than positive number okay you will be smiling all the way but if your mathematics you get a uh your teacher minus your marks until there's no more marks left you will be having a St space teacher teacher IM teacher there is a question from car hi teacher can I know how to determine range and domain without using graph okay that one I will you will need to learn that uh I will need to give you another lesson for that okay so because without actually okay you have the uh arithmetic technique but algebraic method okay we call it the algebraic method if you use that actually it is harder to do the domain and the range then when you sketch a graph believe me if you do a lot of graphing already graph will come out very fast graph will come out very fast and from the graph you will see the domain and the range right in front of your eyes and when you write the answer there won't be any mistake okay but another question from La U teacher the answer is always start from the negative Infinity to positive Infinity uh not all not all for the case that I'm because this I'm doing the basic graph okay basic graph usually uh for straight line for uh Square it is still positive Infinity to negative Infinity let me show you okay like for this one for this one the on the the value the graph is sitting right on top of the for the xaxis so all the domain will be there all those value over there so the the domain of this graph is is still negative Infinity to positive Infinity however the range is different okay the range is different because the range here is going upwards okay there is no numbers at the bottom there's no number at the bottom so this value here from this starting point here this minimum Point here that number is zero that number is zero so our range will start from zero and then comma and then it will involve all the numbers on top of the Y on top of the a x AIS so it will be like all those numbers on the y axis so here I have Infinity okay here I have Infinity because it won't stop this the leg of this one will not stop so what should I put here is it a round or a square for this case because zero is the starting point so I will start with a square why I put a square because there's no number below zero because this is a x squ all number are positive answer and zero are also included because if you put zero squared there is also an answer but for the other end I have to put round brackets because there is no ending on the other side okay so now for this case for this case if I want to write them I want to write them in the format of not uh set okay I want to write this in set so I will have to write like this okay my y because this is range range is y then I have a colon there and I will write this y okay have to be bigger and equals to zero then I close this right or if I want to talk about the element of I also can talk about the element of okay if you want if you just leave your answer like this is you also will get marks later you will see I have one question this one the domain and range they most of the time they carry one or two marks so if they ask for domain or they ask for range that will be it okay so this one if they write in set notation okay how about this one this one according to this question according to this question it is from the uh top here for my domain is all over there and there so it is still negative Infinity to positive Infinity but for my range is from zero until the bottom so bottom means I need to start from uh it will start from zero until negative Infinity okay so it will be from I will write Nega usually the small number is on the left and the the big number is on the right so for this case the small number is negative infinity and the big number is zero okay and then I will close the bracket to know that it stops at zero it won't go any further than that okay so this is for the quadratic uh graph now why do I say just now quadratic graph you need to be careful why do I say that well quadratic graph I need to be careful because quadratic graph involve involve minimum and maximum points okay so whenever you do any quadratic equation it is best to know what where is the minimum Point first or where is the maximum Point first because you have to make sure the curve is uh you can either see the minim whether the minimum point or maximum point is in within what we the range that we want or is just a tiny bit of tail here that we need or a full curve okay or a full curve so we have to be very careful like for this case it's a full curve because this is x square graph but sometimes it is not okay sometimes it is not all right so that and then another thing sometimes quadratic graph will move to the left or move to the right so it will involve some intersection points okay now let me continue if I have a cubic graph I when I have a cubic graph I will be having like if I want the domain of this cubic graph if I want the domain it will involve all over there and all over there so again it will give me from negative Infinity to positive Infinity but and if I want the range is also going up and coming down so it will also involve negative Infinity to positive Infinity okay but if I uh of course for cubic if I want the negative side of the cubic it reflects anything with a negative it reflects so my cubic will look like this oops okay my cubic will look look like this it will I can't seems to be getting it into the zero yes okay the cubic will look like that so it has to like touch the zero because I don't have anything over that side so it has to like move to the zero and again if you look at the Domain it will involve all on the xaxis so it's X until positive and it involve all from the the bottom so it is going to be from uh POS negative Infinity to positive Infinity okay that is cubic graph let's go for this type of graph modulus graph now modulus graph it will involve the modulus modulus means it is talking about the X inside so when I have a modulus graph the basic graph is a v okay the basic graph is a v so the domain will be all on the xaxis all on the x-axis so again when I want to write the domain is going to be negative Infinity to positive Infinity however when I want to write the range same like the case just now I start from zero here until up there okay so which means the range is going to be from zero until positive Infinity so the small number is zero so I will start from zero and the big number on top there is all infinity and infinity have no limit so my range is round okay now I we do have question modulus Nega X inside here so but I'm not going to talk about this because I'm going to talk about the a reflection on so I have here negative of the modulus graph so the negative of this modulus graph means it will reflect on the xaxis so the modulus graph will have a negative value okay so it will look like this okay it will look like this so the negative of the modulus graph is reflected on the x axis okay it's reflected on the xaxis and it uh okay remember it has to start from zero here okay uh the thing is kind of out of control so I like draw it out of the way it's supposed to start from zero so from zero until downwards so the domain is still the same from negative Infinity to positive Infinity but the range is to the to the end okay so it will start from zero and it will end it will start from zero and it end with negative Infinity so I will need to write remember we always write the small one first so the negative Infinity will come first the small number is on the left and the big number is on the right so over here we write a zero and it will close up like that okay so that will give you from here until nonstop the small number is negative Infinity so we write the small number first followed by the big number okay so let's talk about reciprocal graph now for reciprocal graph we have uh two sides like this okay we learned this in your form five so the negative of this reciprocal graph the negative of this reciprocal graph will be on the this side here like this and over this side okay now I need to remind you something about reciprocal graph so let me get rid of this for a while let me get rid of this okay let's say for reciprocal graph okay for reciprocal graph uh let me get rid of that also now let's say for reciprocal graph you accidentally touch the xaxis and you accidentally touch the y a uh the X and the y axis like this you will m we you will get Max minus you cannot reciprocal graph comes with asymptotes it has a horizontal and vertical ASM toote so which means whatever you do your graph cannot touch the ASM toote ASM toote means the line that you cannot the graph could can will never reach why the graph can never reach zero because it if it is zero the function is uh undefined so you cannot touch one more thing let's say okay let me get rid of that too okay let's say if you are reciprocal graph this one is correct already and then suddenly when you reach at the bottom here then you have a curve go up okay let's say if you have a tiny beanie curve going up there that also will not be considered a reciprocal graph okay even even if your curve is a tiny beanie skinny weenie curve like this means the the perer can see the tail going up you will lose Mark too okay so please be careful of what you draw it has to be perfectly following the line and it cannot touch the line it is supposed to be a smooth curve let me try again let me try again later you all make complaints on me know it's still crook okay okay so this already draw a crooked line oh well let's talk about the domain now for according to this question the domain is from here until there and the domain is from here until there you teacher okay there is a question from LA J you teacher is it necessary to label everything on the graph sketch is it yes yes wait I will all right now I I will answer that after I finish this domain let me finish first okay so according to this question okay uh label yeah right yes so what you need to know is when you sketch a graph it is necessary to label for example here I didn't have the zero there okay why I say that okay if you look at your stpm paper you will notice that sketching of graph involve three marks okay three marks most of the question involve three marks one Mark they will give for the curve one Mark is always for the curve or the lines or whatever that they ask you to draw okay whether it's a curve or a line all uh uh analytic geometry ellipse uh Circle Parabola and so on okay that is the curve one Mark you get the shape correct you get the shape correct they will give you one Mark okay second marks is they will be looking for intersection points maybe there is intersection points and the all those uh maximum minimum point intersection point point the details for the graph they will give you marks for the details view the details of the graph and lastly that is one mark for all correct okay that is one mark for all correct all correct means all the things are labeled for example if you want to draw this graph actually this one still cannot get a full marks why I say so because I didn't label FX = to 1/x I did not label that if I did not label that I the peror assume I don't know what is that okay so especially when you are sketching graph that this is basic graph everybody know this is ay focal graph but there are sometimes graph that like for example when you're are doing like a semester two oh semester two you build you have beautiful beautiful sketch that in uh different s that time you might have different different uh labels because all even even uh this chapter this chapter piecewise the piecewise where you have a function one function two function three and you are supposed to put them together into one graph that also you need to label because sometimes you will get a straight line sometimes you will get a curve you sometimes the straight line will join to the curve sometimes they don't join to the Curve Cur so you have to label the graph okay so I need to continue is already 440 oh my God why is the time fly why time flies okay now the domain is here zero is not included so I will have from negative Infinity I will start from the small number so I have negative Infinity zero is not included so I have round okay zero is not included so it all the x-axis here and all there so it is not including this zero y equal uh xal to 0 so zero is not included so how we combine with the next one the next one we put a union or we put a or okay you can put a union okay Union or or you can put either one the other side will start from zero round bracket zero until positive infinity and it is rounded okay and the range also same the range is also same I will have negative Infinity until zero and then or and I will have the other one will be or I can write Union like I say just now from zero until neg uh until positive Infinity okay if I want to write this uh in the form of in the form of set so this will give me X because this is domain so I have colon and then I have uh my X is less not equals to no equals to if you put equals to then it's wrong okay less than zero and or you will have X bigger than zero than the set notation the Y are for the range it will be at from the Y there it will be the almost the same okay so that is the X only for the range you will write Y and then colon and then you say the Y is less than zero again you cannot put equals to because zero is not included so you put all and then you will write Y which is bigger than zero and then you close the the set notation okay so for this one for this one when you want the domain it also will be the same okay it will be exactly the same like here so you will have negative Infinity to zero and then uh if just now I put the all there now I write the union so you either can put both of the uh either one of them don't go and put both of them so you have from zero to positive infinity and over this side it involve all on on top there so it will be from negative Infinity to zero Union with 0 until positive Infinity all rounded no Square why because the the zero here is not included so you cannot put a square okay so that is reciprocal graph next thing let's talk about the uh square root graph okay the square graph for the square graph it has uh is on moving to the right hand side like that so for the negative ones for the negative ones you will have a graph at the bottom okay at the bottom so it will involve the here the Reflection from the bottom like this okay so so this will be your FX = to root of x okay so it's a reflection on the xais so let's write the domain you can try it out okay you can try in on the piece of paper try to write the domain so here it start from zero teer yes what if you let the students to try first before you further with the explanation yeah sure why not one minute break yes let's do so you can play online Puma onlinea www. Academy [Music] YouTuber Academy YouTuber [Music] www. Academy [Music] YouTuber online Puma Academy [Music] YouTuber yay I'm back am I yes yes continue yes yes let's let's continue I hope you got the answer already so I need the domain right so when I need the domain what I'm going to do will be what I'm going to do is I need to look at my x axis so the x-axis start from zero so I will start from zero and I will put a square why because square root of x in involve this zero so it start from zero and it will go to positive Infinity okay that's my domain if you I want to write in set also can now if I want the Y AIS so I will look at the Y AIS and again for the range I have the same answer why because it will start from zero until the top so it will start from zero until positive Infinity okay let's say if I want to sketch the negative one so it will reflect on the x axis when it reflects on the x-axis this will give me uh the domain is starting from zero again so I will start like zero until it's all positive okay it's all positive so I have positive Infinity but when I talk about the range I have a different answer why because it will start from zero but it is going downwards downwards means it's all negative so I always start from the smaller number so it's a negative infinity and it will end up with zero it will stop there and that will be a square brackets any questions should be okay check your answer I'm I bet you are correct okay it's you are we because we are just talking about the basic graph okay next type of graph h ah we did this already so let's go on okay the next type of graph we have the graph with a reciprocal Square when we have a reciprocal squar means we have 1 / X squ all these are basic graph okay only sometimes they have extras in the basic graph so I have 1 / x² so when we want to talk about the domain of 1 /x2 so we talk about over here it all involve from zero here all over and here all over when so when we talk about the domain we are actually involving everything okay except what except here right except this line it cannot be zero why it cannot be zero if this is zero the function fun does not exist okay so if it is zero the function does not exist so this answer is going to be from negative Infinity to zero zero not included and then or I can write all and then I will start back from zero and then I will say that it is infinity on the other side okay how about this one okay it involve all the one on top so that will be positive Infinity but however this line cannot touch here okay the this line will be like from zero until positive Infinity this answer only got one side because both of them is on top of the Y uh on top of the xaxis is all to the portion okay so what I will do is I will write from zero it cannot touch zero and it will involve positive Infinity okay so my range this time is zero until positive Infinity Okay carry on if I have a like this so the domain for this one the domain will involve everything from negative in Infinity to positive Infinity all that over there and it will involve all the Y also so I will have from negative Infinity to positive Infinity I'm speeding I'm speeding I'm driving a turble car now okay for this one cubic with a square I have a like a fountain looking graph so from here this is is included okay so my domain is everything there so everything there and everything there so it's negative Infinity to infinity and my range I have to be careful zero can I put it in yes because if 0 squared will be zero square root will be zero so zero is the an part of the answer so I have zero until positive Infinity round okay so that will be the graph function for cubic and X squ okay square root of x squ Cube uh square root cubic of what am I talking cubic of with the X squ inside that okay so now there is another type of special graph which is your a s minus x² graph okay a s minus x² graph is special a bit because the meain here okay if you uh saw did this graph before here will be negative a and here will be a so the domain will involve this all that until there so when you write the answer it will actually be it will be actually be negative uh a until a close both included but the range is going to be from zero the top portion only the top portion only so from here until the top until here and this because this is a square so this is supposed to be a also here okay the value so it's going to be from zero until a so I will write here zero is included and then until the top the number is a and a is also included okay this one is special type of graph okay it will stop at a there why I know is a because it is actually uh something I can get from here okay uh how for example I give you an example for you to be able to see the question is for example 9 - x² okay 9 - x 2 so this will be like square root of 3 - - x² uh 3 2 - X2 so you will get the number there so how I know got positive negative I just take my x² - 9 = 0 X2 = 9 and my X is equals to + - 3 so that's how I know you I have a A3 here and a three there it's a half it's a semicircle graph okay this is a formula of a semicircle if you already gone your teacher already taught you analytic geometry you should be Familiar of this shape okay well now let's talk about transformation of the graph if I could not finish this week maybe I will continue next week with the same uh format okay of sketching of graph maybe I will include the uh what you call that the exponent and the uh lawn and then uh trigonometry okay you if you like it just leave a comment in the chat box if you want it if you don't want then we Skip and we go to the next one right now the rule of sketching of graph is if you have a function and you have a plus uh or minus when you have a plus for a certain function the graph is is actually moving up okay so if you have a function and you have a plus the graph is moving up if you have a function and you have a minus the function that I'm talking about is the original function okay the original function if you have a minus the graph is moving down if you have like the x is Plus or the x is minus then the graph is actually if that is a plus on the X the graph is actually moving to the left why do I say so if you look at this if I have my X+ C = to Z my X is actually minus away this is a minus C okay so I have here if I have my x - c = to Z my X is actually plus C okay so it is a value from the right hand side graph will be moving to the right hand side let's check it out I I I give this simple one uh do not put up so high hope uh this type of question uh simple one I just want you to see whether it's moving up or moving down only okay this type of question uh so far will not come out for your stpm because it's too easy okay so remember if I have the function so now I'm talking about the function the function now is X squ I get rid of of the earphone all right the function is x s so the function is x s and then I have a plus means my graph is moving up so when I have + one the original is zero here when I have plus one My Graph will be moving upwards okay when I have a function plus means moving up on the function so this graph here I have to understand now where is my Cur okay so it will be moving up here so I need a intersection point over there so what is this intersection point it will be one so you need to label it you need to label your XY your the name of the function and the intersection Point okay let's say if I have a minus a minus means the function is moving down so if the function X the function the original function is x² it is minus so the function is moving downwards so it is moving downwards like that so over here is going to be1 okay now just now I showed you already you when you have x + one so the original graph actually are talking about this whole thing okay the original graph squar so when I have x + 1 means my graph will be like x + 1 = 0 x = to -1 My Graph will start from1 so1 is over here so I will Mark as ne1 I know this whole thing is squared so it is actually comparing to the original graph so my graph will be like this and it will cut somewhere here so oops I have to like make sure it touches the I don't don't have much time so it has to touch the xaxis yeah it has to touch the x-axis so it and it has to be a smooth graph you cannot do crooked things like this okay but I'm rushing for time that's why I'm like uh going faster so so how I know what is the intersection point so when this is x equals to 0 so 0 one 0 + 1 I got one one squ is one so I know this is one okay so if I have X - 1 so I have X - 1 = 0 x = 1 so you know the graph will touch at one here when X = to 1 so again this will be a Smalling graph because in front here is a a is one so I will have a graph that again it has to touch the x-axis okay and it will cut again at X = to 0 so1 one squar you will have one here so you will label everything nicely okay so I will have uh this one when we we have to know if the function so you have to recognize the basic function okay let's see another one let's see another one one one minute more yes almost time one minute more uh okay so I don't have time yeah maybe you can discuss this next week yes I can discuss this next week follow if you want uh an exponential La uh trigonometric graph please leave a comment below so that I know you need it if you find that this is uh I I already know all this I don't need this teacher I only want to talk about uh how to answer stbm question you also can leave a comment in the chat okay so I guess I will actually I have uh actually one more which is the paral question 2017 uh question but never mind you can check it out you can go and look at the question screenshot look at the question try it first next week I will discuss it okay and then well the the time passes too fast scan and vote for me good luck and go get your a right bye see you next week bye-bye okay alhamdulillah finally we have done with today's lesson we learn a lot from teacher IM right congratulation to those who are able to follow our session from the beginning until the end and thank you very much to teacher IM for such an interesting lesson okay for your information Academy YouTuber Malaysia together with clab Guru Malaysia and Ed Malaysia are working hard to provide free tuition for the pupils across Malaysia I repeat pre tution so don't waste this opportunity if you want to get more information regarding classes check out this link www.academy.com okay the link for the certificate is already in the chat session or not yet uh please past the link posing it right now okay okay so um okay okay the password was given throughout the session so we are not going to mention the password again right here if you want you can scroll back to look for the password if you miss it next uh next time you have to join from the beginning yeah yes correct that's correct okay so okay the link for the certificate is ready already in the chat section oh yes uh Yan Shan uh you can use your your your your email your number Emil still can use okay you still can use your email yeah l i m Au U yes yes capital letter l i m a u capital letter okay yes capital letter please okay so um and it will will will only be active for 30 minutes 30 minutes from now okay please click the link no correction is allowed for wrongly type your email or your name okay so once again I would like to thank teacher IM for the interesting lesson boys and girl please support teacher IM Lesson by clicking the Subscribe button please uh uh click the Subscribe button please now okay now okay for the letter list of uh classes you can check www Academy youtube.com Okay that's all bye thank you very much bye bye [Music] [Music] CL [Music] Academy YouTuber Malaysia [Music] [Music] in [Music] www.academy.com Academy