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Pre-Algebra 1.4 - Ordered Pairs and Relations

Added Sep 02, 2020 •

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Be able to graph a set of ordered pairs (x, y) Be able to place a set of ordered pairs into a T-Chart Find Domain and Range

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the technical term people of the switchover once they get their precalculus activist the Cartesian plane if you ever hear the Perky's it's Descartes it's a scientist a mathematical person is a math person let's just go with that you can become a math teacher why don't become me he's look at his face don't look at this don't look at the screen right here find it don't become a math teacher do anything make my math teacher your certified weird certified do anything else don't be me but but if you want to be we're just like me sure go ahead true you can do that all those are great options of using math some people say can I become a chemist can I be a doctor and then submit said Avett all of those are using math instead of just teaching math so much better so much better you're out there doing something for the world all right so always has a story of what all the point of any of this stuff is and the real life concept even though it's just a fake a little story like on You Know PBS Brenna is planning a treasure hunt for her little sister in their yard she has drawn and a grid over the area for the hunt is located two units over East and one unit up north on the grid from the starting point name 00 this location will be named to one on the list of Clues you have a grid and this right here is just a quadrant one so she go over to forgiveness goes over to East and up on North there's two one from there it's up to you to decide what it's up to her to decide does she go with starting with clue one from there to there or does it based on the starting point but in math we always bass it every new plant comes back to the starting point it's a weird thing but down the line to talk to you flow where it goes from one point to the next point to the next point but let's focus on this all right look at this vocabulary all right so we got coordinate system coordinate plane that's in the name for the Cartesian plane coordinate plane x y axis and x axis origin y-axis my fault I'm dyslexic cuz I looked down here x axis ordered pair x coordinate y coordinate there's another term for X and Y will go over that later graph relation domain range all right so when we talked for these right here for 1 do matter so what was this x axis versus y x axis is left to right I will always live with this and all it is the number line this is only some people bother with this I don't bother with it at that much but I'll do it for now X+ on this side x negative on this side if you don't know that's the number line right there then then you have the up and down number line which is your y axis DIY positive y negative all it is is a number line and right smack-dab in the center right here is your origin you got zero zero 0x 0y all your ordered pairs is it all your ordered pairs call the order of X then y so that's the X number so this pretty much the X and Y is at 0 0 now couple different thing so one thing that's not mentioned are quadrants so when it's positive positive is the positive positive quadrant is it called quadrant one rent 1 quadrant 1 and 3 Noah never messes up cuz if you count if you go this way clockwise or counterclockwise you don't mess up two of them I was just so this right here is the negative negative quadrant in this is quadrant 3 1 + 3 no one ever messes up but you need to know the quadrants go counter-clockwise eating backwards in time what's up question Quadrant 4 Milton Squadron to my fault two and four other ones get mixed up to 1 2 3 4 1 2 3 4 1 and 3 hours stay the same two and Fords were people get mixed up so it's counterclockwise so this right here is that negative positive and then this right here is the positive negative last one positive negative Quadrant 4 for some reason a lot of textbooks skip this idea it's a simple description but they skip it so quadrant it's used to it pretty much what this is this is a airplane again sorry this is a positive positive so here's your origin going up north positive why you're going to the in a right East word positive number line on EXO's positive positive but quadrant 1 2 3 4 all right so remember all your ordered pair text why is it always X Y I know but it's alphabetical order sometimes it Go ABCD but standard is XY all right there's one right here in an equation I'm jumping way ahead so this right here ex tells you what why becomes so this right here is in this extra independent very honorable what that means is independent you can be anything you want your Independence whereas why is called the dependent variable because usually it's in some equation you have some equation like to expose 4 equals y why is dependent on what x does that expression to come out for someone so it's out the plug in an ex that tells you what why is that independent versus dependent so that's that when you try and think what else there is the overall these things we come to it and then you have a list a list of points so just to go is x axis Y axis ordered pair x coordinate y coordinate and I didn't put this care if you don't see that this is your x coordinate a short-handed this is your y coordinate a coordinate is just one number inside a point to coordinates make a point that's another one make 1.2 coordinates one point now when you have a set of points we usually put them in a t-chart so last night before we just move on with all that stuff right there or be quick so we usually get it X and Y here's another thing right here all of this side right here this is I should have made a little bit more space my fault this color X domain all Lexus is called domain and why is your range all your wise all right it's just a list of all your exes a list of all your wise domain and range let's go move on quickly through this stuff right here so setting all this stuff the vocabulary ideas now it's going to actually see it in action all right so focus on why find find clue to on the grid name this location using the method used for clue one alright so look at the method so we all got different ways of explaining it clear one is located two units in one unit of north on the grid Orient Point Zero so this is just getting you to use idea so based on one started 00 starting point so we go over then up 123 so we go 3 units East 2 units North 23 is located at 24 describe the location on the grid who 3 is it 3 or strain so cool three isn't even on here so you put it on to 4 so you go east to one to the North Fork 1234 it's right next to the tree so it's above clue one to the left of clue for by blah blah blah so you just describing it described how to get from clue three to clue for so clue 3 was right here search for you go and here's a thing you always want to go left to right first so this is how it or destroy me even though I could go up one then over true enter the coordinate plane what is go horizontal and vertical SEFCU threes right here we would go east to units from clue three then North one unit and you'll be a clue for so that would be talking like that to get 5 go to unit South and one unit name the location so the locations are always named based on the origin so let's start at 4 to get the clue 5 you go to YouTube South 1/2 and then one unit West so I hear the one unit above clue to so that's one two three so the three 33 with a clue it's all these different things to do  what's the right let's just move on in mathematics a coordinate system or coordinate plane is used to locate points the coordinate system is the intersection of two number lines that meet at right angles at their zero points so x axis y-axis origins or zero ready whenever that an ordered pair numbers is used to locate any point on a coordinate plane number is called the x coordinate in the second number is called the y coordinate so x and y coordinate and again if you have a list of the list of exes that you don't list of wise range we're going to get to that don't come of that simple enough hopefully you seen this before if not please let me know so to graph an ordered pair call a. At point that corresponds to the ordered pair so are your directions to locate the point so let's go this study tip coordinate planes unless they are marked otherwise you can each unit on the x-axis and y-axis represents one what they're saying right there is you don't have to follow the number life but if nothing is marked what's use the quadrant one your X & Y axis are technically independent of each other in terms of how you Nuremberg so when you guys get the business you want to talk based in some like thousand so thousand the money you always want to see money right so that's using your y coordinate and time is your ex so what business is based on months or months is based on one so you counted as one 34 but in business you're mm of dollars so you don't want to go watch a thousand they count with thousands so you don't have to follow the same numbering system on the XY axis is what this is saying you could do any system you want as long as it's equally spaced so this will the y axis is based on thousands this is based on one but you still find the graphs in the coordinates the same way in one month it's at $2,000 in two months it's at 1500 there's no 1500 but you know it's some exactly in the middle you know in 3 months. 0 in 4 months got 500 that's the idea graph each ordered pair start at the origin five 3 so text Courtney move over 5 so you always go horizontal first and then it says the coordinate is three three up from that spot so 304 don't go anywhere on your x-axis what should 2nd number so why you go up for so yes let that she bother with this cuz I didn't give you guys any graph unless you have graph paper why but let's do this one together. Tell her I'm going to show you it doesn't matter as long as you got somewhat steady enough hands you can make your own grid and it's getting us so just go faster this is straight but it's tilted slightly you can kind of see that compared to this this right here got straight so down here kind of went down and wavered that's okay you just doing a sketch of all of you to 253 and 6 1/2 will hey let's go let's go all the way up to 7 the eyeball it close enough here's my one 2 3 4 5 6 7 show me to number the mall number enough of them so I can figure out where they are so based on my wise I got a 301 and 1/2 5 and 1/2 so let's go up to six 1 2 3 4 5 6 and this is good enough to find every single one of these points this one a 1 b 1 c 1 B does call ABCD easy enough so to 3 I go over to then up 31233 is about here call that my a that's when I go over 5 units zero I still stand or go anywhere on my why so go over 5 with you here is C3 you go on the x-axis 3 x + 1 and 1/2 on the wall 31 is right here to is right there till 1 and 1/2 is in between that 6 1/2 five and a half so here's 6 1/2 is here 5 and a half would be right there I don't have grass paper but I was still able to label my ABCD points using these coordinates Johnny graph paper but with that said if you want to be exact sure use graph paper you should but that's basics of graphing so naming points so this right here be the more common thing naming the coordinate knowing where the points is just going backwards I give you a graph name every single coordinate so a what is a so you don't start going up and down you always go horizontal Donald Denver tackle so we go over one two one two three four five six so to six point point D you go over 1 at all so it's 3 0 re zero see you don't go left or right you don't go horizontal or are you just on the Wireline so 01202 0 to 4 point seat 1 2 3 4 5 6 2 6 on your ex 123 634d graphing or naming points pretty much similar things right now a relation is a set of ordered pairs such as 233 54156 is a relation so set of numbers a dataset call the relation is this premise long is the word set a group a group of numbers a set of ordered pairs is relation so pretty much just saying these points are a relation because they're on the same graph this relationship what go back what use English again Lexile a relation what is your relationship with blank and blank your relationship in your house is either child sibling cousin sometimes your cousins live with you nephew niece I want some guys are on some guys even Nobles what's your relation with all the different people at school what's the relation was that group there in my loc class in that class this class pre-algebra class it's how you're connected so all of these points are connected on the same graph use your vocabulary of your previous knowledge of vocabulary things how are all these things connected the connections on the same graph a relation can also be shown in a table or a graph the domain every other relation is the set of x coordinates the range a relation is the set of y coordinate so domain and range and domain and range is also called input-output so we got another name right there so here let's list is your relation I'm giving it a variable Capital there but when you have a set of relations you give a capybara book are and if using instead of parentheses I can't really draw and then they give you prices to three 3 V for 1 five 6 and then a close enough another bracket you don't have to do this but in the beginning cuz it's long enough it's safe to do this XY XY XY XY doesn't want to set it now I'm going to do two different ways I am one of those people that like a top-down format I always go XYZ Play I'm Leaving space cuz we have other names for it remember I said independent and dependent I'm shorthanded because I don't want to write the whole word we also called this domain Russell called this the rain this last time we just saw it right here it's also called the input it's also the outfit all these different names you got to know the difference no all you do is just list of points separate them so X and Y this follows this format just separate it to 335-4156 you can do it this way but some people still do it this way which is perfectly fine a horizontal chart but then if you do it like that it's 2/3 free five for 1 5 6 reasons why people like this one better than this one it's just a simple thing easy to list go left to right reading top down for a lot of people of spunky so if it ask for your domain your domain give me all your domain numbers what's domain again domain is your ex your domain is the set of all the numbers that are exes 2345 if they ask you to list it it's just a list of all your wine them and so this method right here and just listed left to right so you know your attitude this right here you got a you know you got to go hear same thing but you know I was going from top down to Left Right some people don't like that 3516 it matches up is it raining now with that said your domain and range there's technically no or you can actually mix all of these up a domain is just a list of all your ex numbers it doesn't have to follow this so sometimes on the SAT they don't have this one right here don't never have both they will never have both when I'm about to do so sometimes we're like I said the SAT or some type of a college question test this year the cancel the SAT do it again anyways sometimes they put it in a sending order so they rearranged all of it even though they put it in you border 1356 remember the range is this a list of the numbers it doesn't have to follow the order that it's coming from in the chart I would not take points off if you wrote this cuz you just wrote that you followed that but because it's a set it doesn't have the fog that doesn't mean to match let's go with that doesn't need to match all right 234-535-1600 tables to different tables I did a top down vertical and also did a horizontal left to right and then it's all the same and then graphing them whatever sore right here all right let's follow this. together cuz even though if you printed this out you heard you see the answer under it express the relation 02142 538 as a table then determine the domain and range super simple the last smartest thing to do is just I should do it in order make a table first Express the relation as a table this will always help you organize it sometimes you guys look at this right here this is just a list of numbers get mixed up easily set it as a table first 02142 538 notice top-down just all right it's super quick me me the way I think faster form at domain range capital D capital r domain and you don't have to write the whole word out and you just do a squiggly line domain is all your ex's 0 1 2 3 range 2458 Sybil what's the work in finding your domain and range your table cuz the table house organized all of this if you want to be more specific you can go domain range cuz your listing Megaman arranged if you want to add that little bit of work but the work is just making a table and seeing what your ranges similar domain 0 1 2 3 range 2458 take a cool 30 seconds the number to be on your own making sure you know what to do 30 seconds I'll give you a minute fine I'll read it you do it express the relation to 403-1411 as a table then determine the domain and range and then simple quick lesson I got 30 seconds to should be done if you're not don't worry math is not a race math is about getting it right but that's the whole sad thing a test your kind you only have the beginning to the end so even though I say time does it matters not race the overall scheme of things yes there is no time but you got to realize you can't spend too much time on this I know it's a hyperbole show me the range make a table x y 24031 411 super-quick your domain 2011 I'm going to do some extra in a second and then your range 4 341 now here's something that you can actually leave out I will never take points away cuz you're just listening it but at a certain point you're listing all different different wise so anything repeated list once if you guys and remember finding the least common multiple using the bubble method you would Circle The Columns of all the different prime factors and then in the ones that have the one in common you only take one of them out so 2018 you don't need it again I will never mark this wrong but for Clara the domain or just all the different a list of all the different exes same thing right here for 3 already got a 4-1 much better it's cleaner we're going she's around like I said of computer programming for some of you guys even though this is the complete with everything from here but this extra one is using extra data space in your programming is your job down same thing with this for those you guys are going to be doing those stem program so some of you guys applied two or three of you guys over the summer for those camps virtual stem camps those are nice things to put on a transcript think about how you okay you guys are in Middle School it doesn't you know it's it doesn't really affect your high school a resume but it helps get you ahead to better camp does you guys want to go to m Caltech in San Luis Obispo what other great Medical School even with that John Muir was at Baltimore Brown University all these camps help you guys helps you network alright real-world usage all right relations as graphs in the real world are the slowest swimming fish do to their unusual body shape that's a lot that's why they hide in those little kelp forest officials can get trapped there because they move so freaking anyway to move flutter their back then up to 35 times per second I saw that I saw that in My Little Pony these are horses Berkeley fin are good school for architecture just to let you know that other school and everybody loves it everybody dogs it is a very good school for architecture and engineering good for sinuses you guys are into BIOS what is a good major to Bean East Bay's a good one I should have went there if you guys want to do music production everybody hears about SF State East Bay is good if you want if you guys watch cop shoot cop shows with all those up police shows where they always got the the Science Guy do all that forensic stuff the CIA and I want to work for the FBI lost track of East Coast yeah it's fun place it's a great School in easy to get into case of what I lesson life lesson all you guys are California residents because you are a California resident all you need you don't even need to take an SAT you don't even need to take whatever entrance college entrance test is sat get rid of they're going to have something else in the future all you guys need to do is maintain a 3.0 GPA on a 4.0 all you need to do is maintain a 3.0 GPA and you are automatically accepted just by bring up the application no essay needed you don't need to write a personal essay 3.0 gets you into any Cal State University what is a Cal State University what's a unweighted just add legit 3.0 straight up you're automatically in include your electives everything you know because unweight is Ice Cube worth more people don't realize get a 3.0 GPA higher classes any cows thing except technically one you can go to in your in the system any school that has an opening that will take you what's a Cal State somebody not UC Berkeley that's a you see that's a University of California cal state is a Cal State University in the name you got Cal State East Bay San Francisco State what is what elevation at San Jose State Sacramento State Cal State Long Beach Cal State LA San Diego State Cal State Northridge those are all CAL States so with in California where one of the that's why a lot of people on the committee why do we have so many universities we have three systems we have a private school private school system which is like a Stanford you know those are pepper guy those are it schools you know we're going to do those all right fine we'll do that Diego Cal State as long as you have a 3.0 and the school is not impacted I'll be over that quickly and impacted is like the most popular schools that everyone everyone wants to go to you need to take the SAT SF State San Diego State Cal State LA translate What other state schools everyone wants to go to Chico State those are like super popular ones so they can only fit so many students then they need the SAT they'll choose the person the best SAT score to get in East Bay this is filling out an application for a job at Humboldt State application because they don't want to go to sfc want to go to San Jose so that then you need like a SAT or something else community service accounts to that's a nice but that's beside the point so all of you every single one of you guys while I'm not this good I'm not that good it doesn't matter if you think that all you need is a 3.0 GPA you are university university quality it's up to you to decide where you want to go some people and say what I want to save money go to community college first that's on you all right back to our Sea Ponies My Little Pony in the sea a seahorse swims at a rate of about 5 feet per hour last step in a second make a table of ordered pairs to in which the exponent represents hours and the wife when it represents the number of feet x hours why feet for Mr flemister this is stuff you guys going to do for science you make me a data chart based on cremations in your reading your your your foe science experiments so is 0 hours how far does the Seahawks game start in one hour it goes 5 feet in 2 hours how far does the summer type it and say it 2 hours how far you go good 1010 good job 223 how far does it go good for Salon in Sulphur I'm going to stop right here this right here is a dentist so in science he's going to ask you to create a hypothesis so you guys observe 1 hour to Arthur I was 4 hours this what are we counting by in the X what what what what number system are we counting by on the X's Warren County bionx hours and number Weis so hours The Hours by what number system what would be the next one we're counting by ones so we go 567 what system are we counting on for wide feet so you can actually figure out all of these you know 5-6 20 25 30 but the further down the line is let's see what would 18 hours be the whole thing is that's why you want to match it up it's proportional some of you guys went over last year remember there's a proportion y equals KX your ex its before everything stays the same and the K in this case is five 0 * 551 * 502 * 503 * 5/4 * 5 * 5 you don't need to count every single one but you can shut up this is how you use it for Science and all that your stem stuff all right B we matched up so they just went 124 124 I just did all of them so it matches up and notice right here it forms a straight line so it's called it's proportional I'm jumping ahead this extra information Pro portion no grass you know it's a proportional graph if you can draw straight line from origin through all points the straight line so from your origin origin through all the points of they only had three but if you go from your words and you can connect it it is a straight line so it's a proportional graph 00 it doesn't have a straight line after all your other points but if it doesn't connect to your origin or one of the points is off it's not proportional so that's another extra bit of information we'll get to that later so you in your classwork homework classwork is just one through eleven simple enough why do guys have already done it fine go in your breakout rooms work together check your answers you know and hey are you gave your answer some you guys got the answers and it doesn't match your answer this is the time to talk amongst your peers and see how they got the answer number I gave you the answer key just got to work all right so is 1/2 a I think we should have went to 11 and then homework doesn't did anybody look at it and say what see what I put on there work to do go back one just went through 11 for class work homework which can also be done now is super quick and easy you do when your break out room help each other out 13235 Todd Dana 35 need help on number 32 and 33 what is 32 AUD no but I'll show it to you anyways just in case 32 and 33 all right I'll just for the heck of it before I throw you in the groups she could figure out 33 on your own use 32 as a model all right let me switch back to this thing all right so 32 the cost of a mini pizza is $7 a piece of pizza that's Little Caesars in town call Little Caesars Pizza I like Little Caesars on my people hate I think it's better than Domino's it's cheaper to and that crazy stuff bread it is the cost of mini pizza is $7 at pita pita make a table of ordered pairs in the which the x coordinate represents the number of mini pizzas and the y-coordinate represented what's a 1/3 and 5 all right so let's do that so X is the number number of pizzas and y equals the cost and that silly that's that doesn't need to be straight it's good enough so what are we doing we're doing one pizza three pieces and 5 so the cost of one pizza is 7 so K is $7 k equals 7 1 * 773 * 7.5 * 7 35 graph the ordered pair. I'm going to do this one right here the graph for you I was using I said I'm not going to bother the graph case in point you shouldn't don't even bother wasting your time so different number lines for you where's my x-axis here's my wife look at this my exes my exes are counting by odd numbers skip to 2 for you know what let's count by odds here's one 3 five is up to you you can still do 1 345 but if you look at your data set 25 I want you to drivelines I know I'm counting by sevens 14 how much easier does soap each number line is independent of each other one and seven 3 + 21 5:35 instead of making 35 live did he say anyways I'm going to send you off into your own groups Now work on this stuff together if you've already done it finished once you guys are done makes to help you all your break out room to get this done its due small groups of three to four people once your group is done you're more than welcome to go to lunch it's not I'm just going to shrink your groups together fine do that alright Joyner rooms join your room

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Pre-Algebra 1.4 - Ordered Pairs and Relations

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