Notation and Quadratics Overview

okay we're live in jackson's room with day two of section one i can write that at the top so this is day two of section one one okay so all we're gonna do today is we're gonna talk about different notation we'll go right on over and we'll go back to some of that vocabulary a little bit and we'll see example six who remembers what example six is we we named it yesterday some of you knew what it was is it linear it's uh quadratic very good so that's not like naming it is not part of our lesson today it is just um solving quadratics all of that stuff so that's a quadratic and we learned that every single quadratic that's u-shaped and upside down has a domain of what what do we learned yesterday the domain for all of these is infinity to negative infinity it's called all real numbers we don't even have to write anything yet maybe just highlight and i already got you started this was one way to write it i already got you in the door with the second way to write it you didn't even know you were learning the next day's lesson the other way to write it was negative infinity to infinity so just fill that in now the name of that is called interval notation so i'll highlight a little interval notation is using these parentheses and today we're going to add some brackets and i'm going to give you a cheat on the side whenever you have um a solid dot you are going to use a bracket whenever you have an open dot you are going to use a parenthesis so what a parenthesis tells me is it doesn't include the value because it's an open dot so we're going to see some overdose and i'll relate it to what's right up above in just a minute and then the other thing is if you have negative infinity or infinity you use parentheses also so today really what you're going to do to get comfortable with interval notation is just get comfortable with those parentheses in those brackets in kind of your big kid notation so i already got you in the door this would be what you probably need from algebra one this is what we did yesterday and then we have one other way to write it so that's really all today is about it really strengthens the yesterday's lesson question so far i gave you a couple little things to put in the corner does anybody need a blank copy of these notes because they forgot theirs just before i get started okay i had somebody like handwriting them out yesterday and i was like oh my gosh i have extras i made like 10 copies so i don't care about the paper so i have to remember everything's being recorded though so be careful what i say i looked at jillian yesterday and i said something i was like oh my gosh i forgot it was being like recorded and she's like it's not that bad i didn't say anything that bad i was like oh my goodness okay so then the third way we write it is called um set builder notation and set builder notation if you look uses those less thans and greater than symbols and we saw those a little bit yesterday so you've already used set builder notation if you go back to like a number line something we should kind of recognize from algebra one and we'll build on an algebra two is if i told you to write this you would go ahead and write it like this you would tell me all of the x's are less than two and you wouldn't put the equal sign because it's an open dot does that make sense to everybody yeah and what's your question yeah yeah i do yeah totally i just thought i filed them away but yeah yeah any time like if you guys forget your notes or something like i don't want you to sit there and not be able to contribute yeah so um so perfect now now you can have a nice copy and that also is the homework behind it it has all the pages from one one so you won't need half of them just throw them in the trash i don't care about paper because some of you someday are going to do something anyone they take this video will be on portal but if you want to take a picture [Music] if you're leaving you're still responsible for it just watch the video or take a picture of the notes on your way out the notes are right there you can take a picture or you can watch the video okay and now i have it recorded that i told you you gotta watch it so don't worry too much today's lighter than yesterday okay interruptions interruptions what can you do you just roll with it right there are bigger issues in life uh-huh my math lesson i gotta tell you i went and saw a friend yesterday and they're having a really big loss in this oh my gosh if anybody wants to move up feel free yeah i didn't even take attendance we'll figure that out after okay so we'll go on with this okay so what we're gonna do is we're gonna take this that we already know and just change it to interval notation so if you look what you can see is you can see this is going on to the negative numbers and the negative numbers are going to be negative infinity have a good one and right here is a 2 so if we wrote it in this interval notation we would write it as negative infinity going to 2. and the reason we would use parentheses is because we can't reach infinity and there's an open circle so you're just learning that notation today how do you guys feel about the three different notations okay and we've seen this one before we've kind of seen with the less friends and greater events okay so we um let's now go ahead and get our third type right here so we know the interval notation and we know how to write it just in words and so what they do is they add this little symbol it looks like an e and the way this is read is the x values are all real numbers so the third way that you can write it this is your third you know way of writing your answer is a r with an extra line um i prefer number two choice i feel like that's the more upper level way of writing it but just in case they use inequalities and an r with an extra line how did you lose your whole class oh you're planning all right okay mr shockton's here i found my water bottle is my husband if nobody knows them this is mr shackton so my class got very small i do not have seven kids i know they just took everybody but i'm recording so they can watch it later so hi everybody mr shakti says hi to you and um okay so now we're going to look at the range so to look at the range we're going to look at the y-axis so if we look at the y-axis what is the smallest or largest value so the smallest if it's like this would be largest if it was upside down you what's the smallest value you guys see for y negative six yeah so we know that negative six is going to be part of our answer remember this is the first way to write it y is less i'm sorry y the least value is negative six and now we'll go ahead and say right here the range is all real numbers that are greater than negative six why would i say greater than because it is going up and where is going up headed to what would we call up here infinity yeah good and if you can like kind of like write these things in the graph then you're just kind of putting those parentheses and brackets around it um so the first way is to just say that all of your y values or your range is greater than negative six and we would just say that the y's are greater than or equal to negative six and they're equal to because it's a solid dot there's actually a point right here at the negative six so that is kind of one of the three ways to go ahead and you know write this that would be like your algebra algebraic notation or your set builder notation i told you this stuff's just kind of boring we're trying to kind of get it together now i'm going to cover up if i had made my own notes i wouldn't have given you the answer but the way you would write this is you would look and see what your smallest number is and since it's negative 6 that would go first this graph is heading to positive infinity and you put a bracket on the negative 6 because it is solid and what would you put around the infinity parenthesis yeah i like the blue and remove on your hair i did green last year and i still have a little bit of um i can tell it's lighter from the bleach i just haven't gotten back but i like the underneath the hair color when people do that i think that's like cool you all of a sudden you see this little trail of like pink coming out from somebody's hair any questions about that these are just the three ways to go ahead and write your answers questions before we move on okay i'm gonna have you guys try one it's a small class so we'll see i'll be able to see if everybody gets it so now what you're gonna do is you're gonna try letters a and b so this is your first one and this is your second one and we're just gonna try to go ahead and get that domain for both of these and i don't care which way you write it i prefer you not write all real numbers and use one of the two notations that you've learned and then um also the range and then if we can get through there we're halfway through this lesson so that will be really really good and we'll be in a good spot i'll give you guys a little bit of music as we're going through and then i'm it's not going to take me long to check everything to see where you guys are at so remember what the arrows mean about the domain and the rings and um is you guys are doing great at this table make sure you look at the y axis okay really good job okay i'm gonna go a little bit further just to make sure you guys are getting this also to get you come to that homework time since you're the ones stuck here with me um what i know is because these arrows go on forever i know visually it looks like it's going like on forever to negative infinity but it's opening up forever this is actually an x to the fourth so what happens is called a quartic function so if you actually took like five and raised it to the fourth it's always how i want my paycheck to be like exponential growth um that's why you can't see that there's actually a point because the point would be all the way down at 625 only for five so like if we went over to five that point would be like way off the graph so that's why you can't see that you can plug in any number you want but when you see the arrows that tells you all real numbers and this is what all real numbers look like okay and then from there we'll go ahead and talk about the range the range you look at the y-axis so i want to go and make sure we're getting this for the people that are going to watch the video later too you're going to look over at the y so who has the range for me for this where is it going from go ahead y is less than or equal to three is perfect did somebody use the interval notation what did we know every you like that okay you use this one too that's not my preference i like the parenthesis one but i'm gonna go ahead and do the parentheses one which is called interval notation so it would be three going to negative infinity but our pre-cal teacher is a stickler on the smaller number going first so think of it as negative infinity going to three what would go around the negative infinity what would go around the three the bracket beautiful now this is kind of cool you might want to write yourself a note in the margin every single line except for uh vertical and horizontal lines what is their domain and range every single time all real numbers yeah so i just kind of think well when i was in algebra one probably one of the first things i learned to graph was a line and so since they're the first thing their domain is always all real numbers you get that from the arrows on both ends but the only exception would be a vertical they can't seem a vertical or horizontal line those would have restrictions on one or the other and we'll see that on that worksheet so don't worry about that how do you guys feel about moving on to one that's like super funky look at this one you're getting like pieces of graphs i know it's like what's going on here right so there's like a part of the graph and another part of the graph and i think i i think this is where it gets a little bit fun and these are called piecewise functions because there's like pieces of them we actually graph them in one slash five so these will actually graph later on with the open circles and stuff so it's kind of neat it's nice that no i don't have to wait for everybody to write down the example we can just go straight on in so we'll go on over and find the domain of this and the range of this function so this right here goes to this graph and then there's one for you to try and that's the end of like the new notes and then i'm just going to review how to graph y equals mx plus b so okay so if we go on over to the domain what i didn't point out is on the last page and i said i don't know why we put it on the three to this page so we don't use it till here but when we have um two sets or two pieces we're going to use a symbol that looks like a u it's a union symbol we're going to be using that to put the two pieces together so maybe a little highlight there we're going to use it right now though so when we go on over we're going to look at both of these chunks individually okay you guys all ready for that so we'll go ahead and we'll look at this piece when we look at it we see there's arrows the arrows tell me what symbol am i probably going to be using the infinity symbol yeah i just had a really nice screen here so as i look at the x-axis i see that i'm coming this part of the graph is coming from this direction you see how we're traveling this what is on this direction of the x-axis what is over here negative infinity yeah so this piece of graph is traveling the x-axis it's coming from negative infinity because we can't look down that's why and where is it stopping on the x-axis yeah why did they make it the same number on the y and the x that's silly and we don't know if you actually got it so when you travel this graph you have to look up here and you see that it's a negative one so this portion goes from negative one i mean i'm sorry negative infinity to negative one what would you put around the negative one a bracket or a parenthesis uh which one one more time a parenthesis so this portion right here is going to be negative infinity going to negative 1 with a parenthesis on both sides then see that u you would add the union symbol because that is just the portion on the left now we're going to jump on the portion that's on the right so we've done this little portion for only domain everybody with me so okay now we jump on this portion we see that it's traveling this direction what is that direction on the x-axis positive infinity and where are we on the x-axis for this piece nice did somebody want to say 2 the other class said 2 because there's more kids but you're at 2 on the y but we're looking at the x so for the x we're at zero so this piece is going to be zero and because it's solid we're gonna make it a bracket and it's gonna go to infinity and that infinity is to have a parenthesis yeah really good you guys are doing good so the domain is all real numbers that are less than negative 1 or greater than or equal to or equal to zero i don't like this fill-in type thing i won't really use it you'll just be writing that's why i'm writing it and like it's totally field i don't know what the word i'm not trying to say but like that's why i'm writing it so you guys kind of see what to expect you won't have like little missing links okay so the x would be less less than um less than not equal to or greater than or equal to and you can pick either one okay now we gotta do the same thing for the range so when we go over the range we're not looking at the x-axis now we're looking at the y-axis any questions so far our eyes are going to this line the y-axis instead of the x again where is this graph coming from when we travel it from it where is this direction negative infinity and it's traveling up in this portion to positive infinity yeah the arrows are still meaning the positive and negative infinities we just are kind of missing a little piece in the section that's causing some constraints or restrictions on the graph so as we're going to negative infinity i travel this and i look at the y-axis where am i on the y-axis negative 1 i would have made that a different number of x and so now i'm going to go ahead and write that i'm going to go from negative infinity to negative 1. they already showed me those of parentheses around it i'm really rewriting the answer what's going to be around the negative one a bracket or a parenthesis on the parentheses good why a parenthesis because it's open dot beautiful this is gonna help the people that have to watch this and teach it to themselves we use the union symbol and then we look at the next chunk the next chunk if we look where are we on the y-axis 2 and we're traveling to [Music] infinity infinity and beyond always makes me think about light here so we're going 2 to infinity and because it's solid we're going to use a bracket so that means the range is all real numbers less than negative 1 and greater [Music] than or equal to 2 and we would use those symbols less than or greater than or equal to 2. that's it so i just need you to try one so i know you've got it so we're gonna do a domain and range question and this is gonna be tricky you're gonna have two pieces for both and the range is super tricky i will not put it on the test but let's see if you can think outside the box with the range because there's an overlap you see how the graph kind of overlap so see if you can get the range if you can't get the range but you get the domain i would be a pig in mud and be the happiest teacher in here oh wait so i didn't mean that who knew i was so funny i didn't even know it so go ahead and try the domain i'm gonna tell you um um um um yeah so what they do is they usually go with um when you're writing these and that interpretation is the smallest number a larger number so because the zero was smaller you now you want to do this okay so let's go ahead and look at this domain of your names i think you probably either at this point or um you're just checking your answers so the domain we go ahead and we jump on the graph at the left we read it left to right that was a really good conversation piece that came out so we get on here and we see that we're coming from negative infinity and we're traveling this graph and we're looking down at the x axis so that would be negative one so it'd be negative infinity to negative 1 with a parenthesis on both sides because of the open circle we put that u in between i don't know if i take off points but i think she wouldn't freak out because you have two pieces to this and then as you jump on this other portion moving left to right you see that you are at positive one on the x-axis but it's solid so you use a bracket and then you're headed to positive infinity and i know the pre-cal teacher is really big on it going in order me i feel like we're still getting to that freak health level i'm a little bit um more lenient on the grading if you had reversed that i probably won't take off points i might just note it okay now for the range this is what i thought the range was i thought the range was negative infinity because we're coming from the bottom and up to one with a parenthesis union um what uh what is this negative one with a bracket going up to infinity and i was wrong anybody else have that same wrong answer yeah what happens is like this would say that there's no numbers between you know um uh negative one one and negative one and isn't there a portion of the graph there this graph filled in this graph it's a really upper level concept so if you look can i travel from negative y and all the way up here and then jump on this portion is there really a break for the y's no so that is not the right answer it's actually all real numbers if that is like what but isn't the y's like when we say this we're saying we don't have a value at one but if i go over to one don't i have a value and i won't put anything tricky like on the test so what i would do is if i was making a test i'd make sure this piece was down lower or this piece was up higher so you truly have a break in your y so don't worry about that too much okay the last thing is i just want to make sure that everybody can graph so for the kids that are out too um and if you've already if you think you already know how to do this try one and then i'll go ahead and um you know you can just be checking this is just do you have a hole in your learning for y equals mx plus b put this okay so this is your algebra one review of y equals mx plus b it will help you with number 25 in the homework that's why i added it and then you need to know that the number in front of x is the slope and the number at the end is called your y-intercept so this is like speedy math we should know this but i pretend everybody's a blank slate everybody that's in here will be able to graph this before you leave because there's only seven of you so we're going to go ahead and then everybody online just make sure you practice and you know what you're doing okay i don't want to go too fast we've got time time's on our side and there's fewer kids you guys are going to probably get to start your homework so that's nice okay so i'm going to do the first one and then you tell me how to do all the others so on the first one i'm going to go ahead and i'm going to first graph the y-intercept what number is the y-intercept 4 so i just go up to 4 and i make a dot if there is a slope i always put it over 1 if i can't see the fraction because you probably remember rise over run if my slope is positive i go up if my slope is negative i go down and i always run to the right and then when kids are comfortable they can go whichever way they want so if you've never been good at this this is how i teach it to kids that struggle in math you're not the struggling kids but maybe this was a hole in your learning maybe you just put it into an app and it did it for you so from the four you're gonna go down because it's negative and over one and the over one is just because any number that's not a for already a fraction is over one and that's all there is to it so okay so we'll just go around and see if we can get a couple of people to help me with this um aiden what's the first thing a number two that i would graph good and what would that value be for this one yeah so we'll go down to negative six and make a dot and then uh where would the slope bring me um thomas where do you think i should go from here good and sometimes they say guys aren't good with directions those are really good directions good don't they say that guys will never stop for directions we shouldn't generalize like that but i'm just being funny yeah don't take anything i say too seriously life is too short to be that serious right okay is there any questions about one or two we're kind of remembering this um brady you want to help me what would you put first on the graph for number three on the y line i like how he said that too he told me exactly where to go a lot of kids put it on the x and it's always the y-intercept and we're talking about x and y intercepts on monday so this is a great read-in and then where would you tell me to go from there you know just stick with me up to and he even gave me good directions up to the right one very good and then um why don't we skip four and just go on down to number eight because number eight looks weird um why is number eight look weird um natalie what's weird about number eight what's myth oh i'm sorry number five number five is weird sorry about it what's weird about number five good so if there's no y intercept what is it it's zero at the origin good words good and then also i don't see a number in front of the x it's a negative one good so we see invisible ones in math all the time i always joke it's an invisible one so then you're gonna go down one and over one really nice job ladies nice job okay and then we'll skip four i'll just put the answer for that for a second in the cycle that will make sure everybody can try one on their own and then another weirdo one is um number six does anybody know how to graph this you want to give it a shot what is the zero though yeah good no no um see how this one um they had the x so the slope is always next to the x so what's missing on this one the x value good go ahead natalie what did you want to add what how would you graph it it's negative seven so that is yeah we go down i have to put on my readers i can't see so two four six so we do go down to negative seven and then natalie do you know what kind of line i make no anybody know what kind of line i made go ahead horizontal yeah when your slope is zero you have a horizontal line so you know how i was saying everybody look up for a second domain and range all real numbers domain and range all real numbers domain and range all real numbers domain and range all numbers almost every line it's all real numbers for domain and range you guys follow me this one is the domain and range all real numbers now the domain is all real numbers but the range is just always negative seven so horizontal and vertical lines are the only exception you know when we're talking about domain names okay i'll fill in four just for the people that are at home and learning can get it do you guys have any questions for me you did so great i always have like candy and stuff i'm gonna buy better like it would have been really boring if they had to just listen to me so it was nice that we had some so take one down pass it around everybody gets a lifesaver you're my lifesavers because you know i would have been talking to myself with seven kids sometimes it doesn't get awkward i'm gonna do number four pause the video at home if you want to try it on your own first that's what's nice about at home learning if it's a video okay there's i put the eight on first i would go down 3 and over 4. and that is our review of how to graph y equals mx plus b so if you don't know that monday and wednesday on after school and today i am not going to make the mistake of forgetting to stop the video so i am going to stop the video before we talk about unrelated to math stuff have a great week

okay we&#39;re live in jackson&#39;s room with day two of section one i can write that at the top so this is day two of section one one okay so all we&#39;re gonna do today is we&#39;re gonna talk about different notation we&#39;ll go right on over and we&#39;ll go back to some of that vocabulary a little bit and we&#39;ll see example six who remembers what example six is we we named it yesterday some of you knew what it was is it linear it&#39;s uh quadratic very good so that&#39;s not like naming it is not part of our lesson today it is just um solving quadratics all of that stuff so that&#39;s a quadratic and we learned that every single quadratic that&#39;s u-shaped and upside down has a domain of what what do we learned yesterday the domain for all of these is infinity to negative infinity it&#39;s called all real numbers we don&#39;t even have to write anything yet maybe just highlight and i already got you started this was one way to write it i already got you in the door with the second way to write it you didn&#39;t even know you were learning the next day&#39;s lesson the other way to write it was negative infinity to infinity so just fill that in now the name of that is called interval notation so i&#39;ll highlight a little interval notation is using these parentheses and today we&#39;re going to add some brackets and i&#39;m going to give you a cheat on the side whenever you have um a solid dot you are going to use a bracket whenever you have an open dot you are going to use a parenthesis so what a parenthesis tells me is it doesn&#39;t include the value because it&#39;s an open dot so we&#39;re going to see some overdose and i&#39;ll relate it to what&#39;s right up above in just a minute and then the other thing is if you have negative infinity or infinity you use parentheses also so today really what you&#39;re going to do to get comfortable with interval notation is just get comfortable with those parentheses in those brackets in kind of your big kid notation so i already got you in the door this would be what you probably need from algebra one this is what we did yesterday and then we have one other way to write it so that&#39;s really all today is about it really strengthens the yesterday&#39;s lesson question so far i gave you a couple little things to put in the corner does anybody need a blank copy of these notes because they forgot theirs just before i get started okay i had somebody like handwriting them out yesterday and i was like oh my gosh i have extras i made like 10 copies so i don&#39;t care about the paper so i have to remember everything&#39;s being recorded though so be careful what i say i looked at jillian yesterday and i said something i was like oh my gosh i forgot it was being like recorded and she&#39;s like it&#39;s not that bad i didn&#39;t say anything that bad i was like oh my goodness okay so then the third way we write it is called um set builder notation and set builder notation if you look uses those less thans and greater than symbols and we saw those a little bit yesterday so you&#39;ve already used set builder notation if you go back to like a number line something we should kind of recognize from algebra one and we&#39;ll build on an algebra two is if i told you to write this you would go ahead and write it like this you would tell me all of the x&#39;s are less than two and you wouldn&#39;t put the equal sign because it&#39;s an open dot does that make sense to everybody yeah and what&#39;s your question yeah yeah i do yeah totally i just thought i filed them away but yeah yeah any time like if you guys forget your notes or something like i don&#39;t want you to sit there and not be able to contribute yeah so um so perfect now now you can have a nice copy and that also is the homework behind it it has all the pages from one one so you won&#39;t need half of them just throw them in the trash i don&#39;t care about paper because some of you someday are going to do something anyone they take this video will be on portal but if you want to take a picture [Music] if you&#39;re leaving you&#39;re still responsible for it just watch the video or take a picture of the notes on your way out the notes are right there you can take a picture or you can watch the video okay and now i have it recorded that i told you you gotta watch it so don&#39;t worry too much today&#39;s lighter than yesterday okay interruptions interruptions what can you do you just roll with it right there are bigger issues in life uh-huh my math lesson i gotta tell you i went and saw a friend yesterday and they&#39;re having a really big loss in this oh my gosh if anybody wants to move up feel free yeah i didn&#39;t even take attendance we&#39;ll figure that out after okay so we&#39;ll go on with this okay so what we&#39;re gonna do is we&#39;re gonna take this that we already know and just change it to interval notation so if you look what you can see is you can see this is going on to the negative numbers and the negative numbers are going to be negative infinity have a good one and right here is a 2 so if we wrote it in this interval notation we would write it as negative infinity going to 2. and the reason we would use parentheses is because we can&#39;t reach infinity and there&#39;s an open circle so you&#39;re just learning that notation today how do you guys feel about the three different notations okay and we&#39;ve seen this one before we&#39;ve kind of seen with the less friends and greater events okay so we um let&#39;s now go ahead and get our third type right here so we know the interval notation and we know how to write it just in words and so what they do is they add this little symbol it looks like an e and the way this is read is the x values are all real numbers so the third way that you can write it this is your third you know way of writing your answer is a r with an extra line um i prefer number two choice i feel like that&#39;s the more upper level way of writing it but just in case they use inequalities and an r with an extra line how did you lose your whole class oh you&#39;re planning all right okay mr shockton&#39;s here i found my water bottle is my husband if nobody knows them this is mr shackton so my class got very small i do not have seven kids i know they just took everybody but i&#39;m recording so they can watch it later so hi everybody mr shakti says hi to you and um okay so now we&#39;re going to look at the range so to look at the range we&#39;re going to look at the y-axis so if we look at the y-axis what is the smallest or largest value so the smallest if it&#39;s like this would be largest if it was upside down you what&#39;s the smallest value you guys see for y negative six yeah so we know that negative six is going to be part of our answer remember this is the first way to write it y is less i&#39;m sorry y the least value is negative six and now we&#39;ll go ahead and say right here the range is all real numbers that are greater than negative six why would i say greater than because it is going up and where is going up headed to what would we call up here infinity yeah good and if you can like kind of like write these things in the graph then you&#39;re just kind of putting those parentheses and brackets around it um so the first way is to just say that all of your y values or your range is greater than negative six and we would just say that the y&#39;s are greater than or equal to negative six and they&#39;re equal to because it&#39;s a solid dot there&#39;s actually a point right here at the negative six so that is kind of one of the three ways to go ahead and you know write this that would be like your algebra algebraic notation or your set builder notation i told you this stuff&#39;s just kind of boring we&#39;re trying to kind of get it together now i&#39;m going to cover up if i had made my own notes i wouldn&#39;t have given you the answer but the way you would write this is you would look and see what your smallest number is and since it&#39;s negative 6 that would go first this graph is heading to positive infinity and you put a bracket on the negative 6 because it is solid and what would you put around the infinity parenthesis yeah i like the blue and remove on your hair i did green last year and i still have a little bit of um i can tell it&#39;s lighter from the bleach i just haven&#39;t gotten back but i like the underneath the hair color when people do that i think that&#39;s like cool you all of a sudden you see this little trail of like pink coming out from somebody&#39;s hair any questions about that these are just the three ways to go ahead and write your answers questions before we move on okay i&#39;m gonna have you guys try one it&#39;s a small class so we&#39;ll see i&#39;ll be able to see if everybody gets it so now what you&#39;re gonna do is you&#39;re gonna try letters a and b so this is your first one and this is your second one and we&#39;re just gonna try to go ahead and get that domain for both of these and i don&#39;t care which way you write it i prefer you not write all real numbers and use one of the two notations that you&#39;ve learned and then um also the range and then if we can get through there we&#39;re halfway through this lesson so that will be really really good and we&#39;ll be in a good spot i&#39;ll give you guys a little bit of music as we&#39;re going through and then i&#39;m it&#39;s not going to take me long to check everything to see where you guys are at so remember what the arrows mean about the domain and the rings and um is you guys are doing great at this table make sure you look at the y axis okay really good job okay i&#39;m gonna go a little bit further just to make sure you guys are getting this also to get you come to that homework time since you&#39;re the ones stuck here with me um what i know is because these arrows go on forever i know visually it looks like it&#39;s going like on forever to negative infinity but it&#39;s opening up forever this is actually an x to the fourth so what happens is called a quartic function so if you actually took like five and raised it to the fourth it&#39;s always how i want my paycheck to be like exponential growth um that&#39;s why you can&#39;t see that there&#39;s actually a point because the point would be all the way down at 625 only for five so like if we went over to five that point would be like way off the graph so that&#39;s why you can&#39;t see that you can plug in any number you want but when you see the arrows that tells you all real numbers and this is what all real numbers look like okay and then from there we&#39;ll go ahead and talk about the range the range you look at the y-axis so i want to go and make sure we&#39;re getting this for the people that are going to watch the video later too you&#39;re going to look over at the y so who has the range for me for this where is it going from go ahead y is less than or equal to three is perfect did somebody use the interval notation what did we know every you like that okay you use this one too that&#39;s not my preference i like the parenthesis one but i&#39;m gonna go ahead and do the parentheses one which is called interval notation so it would be three going to negative infinity but our pre-cal teacher is a stickler on the smaller number going first so think of it as negative infinity going to three what would go around the negative infinity what would go around the three the bracket beautiful now this is kind of cool you might want to write yourself a note in the margin every single line except for uh vertical and horizontal lines what is their domain and range every single time all real numbers yeah so i just kind of think well when i was in algebra one probably one of the first things i learned to graph was a line and so since they&#39;re the first thing their domain is always all real numbers you get that from the arrows on both ends but the only exception would be a vertical they can&#39;t seem a vertical or horizontal line those would have restrictions on one or the other and we&#39;ll see that on that worksheet so don&#39;t worry about that how do you guys feel about moving on to one that&#39;s like super funky look at this one you&#39;re getting like pieces of graphs i know it&#39;s like what&#39;s going on here right so there&#39;s like a part of the graph and another part of the graph and i think i i think this is where it gets a little bit fun and these are called piecewise functions because there&#39;s like pieces of them we actually graph them in one slash five so these will actually graph later on with the open circles and stuff so it&#39;s kind of neat it&#39;s nice that no i don&#39;t have to wait for everybody to write down the example we can just go straight on in so we&#39;ll go on over and find the domain of this and the range of this function so this right here goes to this graph and then there&#39;s one for you to try and that&#39;s the end of like the new notes and then i&#39;m just going to review how to graph y equals mx plus b so okay so if we go on over to the domain what i didn&#39;t point out is on the last page and i said i don&#39;t know why we put it on the three to this page so we don&#39;t use it till here but when we have um two sets or two pieces we&#39;re going to use a symbol that looks like a u it&#39;s a union symbol we&#39;re going to be using that to put the two pieces together so maybe a little highlight there we&#39;re going to use it right now though so when we go on over we&#39;re going to look at both of these chunks individually okay you guys all ready for that so we&#39;ll go ahead and we&#39;ll look at this piece when we look at it we see there&#39;s arrows the arrows tell me what symbol am i probably going to be using the infinity symbol yeah i just had a really nice screen here so as i look at the x-axis i see that i&#39;m coming this part of the graph is coming from this direction you see how we&#39;re traveling this what is on this direction of the x-axis what is over here negative infinity yeah so this piece of graph is traveling the x-axis it&#39;s coming from negative infinity because we can&#39;t look down that&#39;s why and where is it stopping on the x-axis yeah why did they make it the same number on the y and the x that&#39;s silly and we don&#39;t know if you actually got it so when you travel this graph you have to look up here and you see that it&#39;s a negative one so this portion goes from negative one i mean i&#39;m sorry negative infinity to negative one what would you put around the negative one a bracket or a parenthesis uh which one one more time a parenthesis so this portion right here is going to be negative infinity going to negative 1 with a parenthesis on both sides then see that u you would add the union symbol because that is just the portion on the left now we&#39;re going to jump on the portion that&#39;s on the right so we&#39;ve done this little portion for only domain everybody with me so okay now we jump on this portion we see that it&#39;s traveling this direction what is that direction on the x-axis positive infinity and where are we on the x-axis for this piece nice did somebody want to say 2 the other class said 2 because there&#39;s more kids but you&#39;re at 2 on the y but we&#39;re looking at the x so for the x we&#39;re at zero so this piece is going to be zero and because it&#39;s solid we&#39;re gonna make it a bracket and it&#39;s gonna go to infinity and that infinity is to have a parenthesis yeah really good you guys are doing good so the domain is all real numbers that are less than negative 1 or greater than or equal to or equal to zero i don&#39;t like this fill-in type thing i won&#39;t really use it you&#39;ll just be writing that&#39;s why i&#39;m writing it and like it&#39;s totally field i don&#39;t know what the word i&#39;m not trying to say but like that&#39;s why i&#39;m writing it so you guys kind of see what to expect you won&#39;t have like little missing links okay so the x would be less less than um less than not equal to or greater than or equal to and you can pick either one okay now we gotta do the same thing for the range so when we go over the range we&#39;re not looking at the x-axis now we&#39;re looking at the y-axis any questions so far our eyes are going to this line the y-axis instead of the x again where is this graph coming from when we travel it from it where is this direction negative infinity and it&#39;s traveling up in this portion to positive infinity yeah the arrows are still meaning the positive and negative infinities we just are kind of missing a little piece in the section that&#39;s causing some constraints or restrictions on the graph so as we&#39;re going to negative infinity i travel this and i look at the y-axis where am i on the y-axis negative 1 i would have made that a different number of x and so now i&#39;m going to go ahead and write that i&#39;m going to go from negative infinity to negative 1. they already showed me those of parentheses around it i&#39;m really rewriting the answer what&#39;s going to be around the negative one a bracket or a parenthesis on the parentheses good why a parenthesis because it&#39;s open dot beautiful this is gonna help the people that have to watch this and teach it to themselves we use the union symbol and then we look at the next chunk the next chunk if we look where are we on the y-axis 2 and we&#39;re traveling to [Music] infinity infinity and beyond always makes me think about light here so we&#39;re going 2 to infinity and because it&#39;s solid we&#39;re going to use a bracket so that means the range is all real numbers less than negative 1 and greater [Music] than or equal to 2 and we would use those symbols less than or greater than or equal to 2. that&#39;s it so i just need you to try one so i know you&#39;ve got it so we&#39;re gonna do a domain and range question and this is gonna be tricky you&#39;re gonna have two pieces for both and the range is super tricky i will not put it on the test but let&#39;s see if you can think outside the box with the range because there&#39;s an overlap you see how the graph kind of overlap so see if you can get the range if you can&#39;t get the range but you get the domain i would be a pig in mud and be the happiest teacher in here oh wait so i didn&#39;t mean that who knew i was so funny i didn&#39;t even know it so go ahead and try the domain i&#39;m gonna tell you um um um um yeah so what they do is they usually go with um when you&#39;re writing these and that interpretation is the smallest number a larger number so because the zero was smaller you now you want to do this okay so let&#39;s go ahead and look at this domain of your names i think you probably either at this point or um you&#39;re just checking your answers so the domain we go ahead and we jump on the graph at the left we read it left to right that was a really good conversation piece that came out so we get on here and we see that we&#39;re coming from negative infinity and we&#39;re traveling this graph and we&#39;re looking down at the x axis so that would be negative one so it&#39;d be negative infinity to negative 1 with a parenthesis on both sides because of the open circle we put that u in between i don&#39;t know if i take off points but i think she wouldn&#39;t freak out because you have two pieces to this and then as you jump on this other portion moving left to right you see that you are at positive one on the x-axis but it&#39;s solid so you use a bracket and then you&#39;re headed to positive infinity and i know the pre-cal teacher is really big on it going in order me i feel like we&#39;re still getting to that freak health level i&#39;m a little bit um more lenient on the grading if you had reversed that i probably won&#39;t take off points i might just note it okay now for the range this is what i thought the range was i thought the range was negative infinity because we&#39;re coming from the bottom and up to one with a parenthesis union um what uh what is this negative one with a bracket going up to infinity and i was wrong anybody else have that same wrong answer yeah what happens is like this would say that there&#39;s no numbers between you know um uh negative one one and negative one and isn&#39;t there a portion of the graph there this graph filled in this graph it&#39;s a really upper level concept so if you look can i travel from negative y and all the way up here and then jump on this portion is there really a break for the y&#39;s no so that is not the right answer it&#39;s actually all real numbers if that is like what but isn&#39;t the y&#39;s like when we say this we&#39;re saying we don&#39;t have a value at one but if i go over to one don&#39;t i have a value and i won&#39;t put anything tricky like on the test so what i would do is if i was making a test i&#39;d make sure this piece was down lower or this piece was up higher so you truly have a break in your y so don&#39;t worry about that too much okay the last thing is i just want to make sure that everybody can graph so for the kids that are out too um and if you&#39;ve already if you think you already know how to do this try one and then i&#39;ll go ahead and um you know you can just be checking this is just do you have a hole in your learning for y equals mx plus b put this okay so this is your algebra one review of y equals mx plus b it will help you with number 25 in the homework that&#39;s why i added it and then you need to know that the number in front of x is the slope and the number at the end is called your y-intercept so this is like speedy math we should know this but i pretend everybody&#39;s a blank slate everybody that&#39;s in here will be able to graph this before you leave because there&#39;s only seven of you so we&#39;re going to go ahead and then everybody online just make sure you practice and you know what you&#39;re doing okay i don&#39;t want to go too fast we&#39;ve got time time&#39;s on our side and there&#39;s fewer kids you guys are going to probably get to start your homework so that&#39;s nice okay so i&#39;m going to do the first one and then you tell me how to do all the others so on the first one i&#39;m going to go ahead and i&#39;m going to first graph the y-intercept what number is the y-intercept 4 so i just go up to 4 and i make a dot if there is a slope i always put it over 1 if i can&#39;t see the fraction because you probably remember rise over run if my slope is positive i go up if my slope is negative i go down and i always run to the right and then when kids are comfortable they can go whichever way they want so if you&#39;ve never been good at this this is how i teach it to kids that struggle in math you&#39;re not the struggling kids but maybe this was a hole in your learning maybe you just put it into an app and it did it for you so from the four you&#39;re gonna go down because it&#39;s negative and over one and the over one is just because any number that&#39;s not a for already a fraction is over one and that&#39;s all there is to it so okay so we&#39;ll just go around and see if we can get a couple of people to help me with this um aiden what&#39;s the first thing a number two that i would graph good and what would that value be for this one yeah so we&#39;ll go down to negative six and make a dot and then uh where would the slope bring me um thomas where do you think i should go from here good and sometimes they say guys aren&#39;t good with directions those are really good directions good don&#39;t they say that guys will never stop for directions we shouldn&#39;t generalize like that but i&#39;m just being funny yeah don&#39;t take anything i say too seriously life is too short to be that serious right okay is there any questions about one or two we&#39;re kind of remembering this um brady you want to help me what would you put first on the graph for number three on the y line i like how he said that too he told me exactly where to go a lot of kids put it on the x and it&#39;s always the y-intercept and we&#39;re talking about x and y intercepts on monday so this is a great read-in and then where would you tell me to go from there you know just stick with me up to and he even gave me good directions up to the right one very good and then um why don&#39;t we skip four and just go on down to number eight because number eight looks weird um why is number eight look weird um natalie what&#39;s weird about number eight what&#39;s myth oh i&#39;m sorry number five number five is weird sorry about it what&#39;s weird about number five good so if there&#39;s no y intercept what is it it&#39;s zero at the origin good words good and then also i don&#39;t see a number in front of the x it&#39;s a negative one good so we see invisible ones in math all the time i always joke it&#39;s an invisible one so then you&#39;re gonna go down one and over one really nice job ladies nice job okay and then we&#39;ll skip four i&#39;ll just put the answer for that for a second in the cycle that will make sure everybody can try one on their own and then another weirdo one is um number six does anybody know how to graph this you want to give it a shot what is the zero though yeah good no no um see how this one um they had the x so the slope is always next to the x so what&#39;s missing on this one the x value good go ahead natalie what did you want to add what how would you graph it it&#39;s negative seven so that is yeah we go down i have to put on my readers i can&#39;t see so two four six so we do go down to negative seven and then natalie do you know what kind of line i make no anybody know what kind of line i made go ahead horizontal yeah when your slope is zero you have a horizontal line so you know how i was saying everybody look up for a second domain and range all real numbers domain and range all real numbers domain and range all real numbers domain and range all numbers almost every line it&#39;s all real numbers for domain and range you guys follow me this one is the domain and range all real numbers now the domain is all real numbers but the range is just always negative seven so horizontal and vertical lines are the only exception you know when we&#39;re talking about domain names okay i&#39;ll fill in four just for the people that are at home and learning can get it do you guys have any questions for me you did so great i always have like candy and stuff i&#39;m gonna buy better like it would have been really boring if they had to just listen to me so it was nice that we had some so take one down pass it around everybody gets a lifesaver you&#39;re my lifesavers because you know i would have been talking to myself with seven kids sometimes it doesn&#39;t get awkward i&#39;m gonna do number four pause the video at home if you want to try it on your own first that&#39;s what&#39;s nice about at home learning if it&#39;s a video okay there&#39;s i put the eight on first i would go down 3 and over 4. and that is our review of how to graph y equals mx plus b so if you don&#39;t know that monday and wednesday on after school and today i am not going to make the mistake of forgetting to stop the video so i am going to stop the video before we talk about unrelated to math stuff have a great week

Transcript for:Notation and Quadratics Overview

Transcript for:
Notation and Quadratics Overview