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Algebra 1 3.7 Review Notes

Added May 21, 2020 •

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Algebra 1 3.7 Review Notes

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morning energy money Algebra 1 we are going to jump straight into revealing. 3.7 please have your paper and pencil ready to go you can go ahead and do the sting cast notes bad today we're going to be graphing absolute value equations okay there's a couple things I we need to know before graphing absolute value equations you might have heard the phrase absolute value inequalities okay when we have to differentiate between the two inequalities adolescent greater than less than equal to or greater than equal to signs OK and the graphs are similar to the absolute value equations if it's absolute value inequalities except that there's going to be shooting involving Russ we're going to focus on the equations equations that lets her know what their parent function of the absolute value equation play this is going to be a parent function which means that this is the most basic absolute value function to come up with the absolute value of a 12 what does that look like the graph actually ends up looking like to do you guys remember going to be appreciate is all the graph that we come across are you going to be v-shaped okay so how do we get that well let's think about this if I were to start from is there going to be my birthday. Which is right here okay and I plug it valleys into the function of absolute value of x + testify take the test negative to negative 1 1 0 1 and 2 0 0 0 1 2 this is one the absolute 2 is too so this is too well it gets different and the reason why the V shape that's the value of one is positive one. Still stays positive the absolute value of -2 is 2 dispositive so let's define absolute value absolute value is not just changing signed to positive and it's not the most accurate description it's a yes it is a version of Apple Valley but we're going to Define it as the distance away from zero so if you're doing this for example if I'm thinking about the absolute value of 5 it exists -5 as well as fine okay those those would be two points that are the same units away from there outside to take both into consideration okay. So let's try graphing list it started with an easy one. Let us we're going to try to use some trim affirmations okay in order to graph so if I had a graph f of x is equal to absolute value of x put two what's going to happen is we'll first of all I have my parent function I hear an absolute value of x and then the plus two shifts all points up to okay so knowing that I'm going to do that I'm going to treat my ex-wife keep trying parent function I'm going to go from negative to negative 1 0 1 2 K I know my vertex is 0 and I'm going to plug in the same values that I did okay which is 21012 I'm going to create another column this time I'm going to put the absolute value of x + 2 sewn to do y + 2 okay when I do that oh no I don't need to do it that way I'm just shifting out of that we don't need to start, I got to pee let's go from here I'm ready to go straight to my graph I'm going to graph these points by x 20 chart right here because I look like this on the right time to 21100 there's my fishing now my left side negative 10122 and that's my grandpa right there but I need to ship all the points up to so I'm going to go up 00 when I go up to here when I'm going to go up to she makes it one three two for this is my new right side of the graph this is menu so that's how that's true let's try another problem what if we have g f x is it Australia x - 3 this is going to let me know that I'm going to end up shifting all the graphs shift all points write three I'll let you two opposite side if it's inside the function I'm usually or parentheses General as you going to do the opposite side okay so against electric my parent function just thought you should be able to memorize this negative to negative 1 0 1 2 and then I'm going to I know that it's 2101 to say nothing but with a graphic I'm going to ship all the boys write 3 so initially this is going to be my graph 1 2 3 same graph as a biggest problem 1 2 3 then I'm going to shift all the point write 3 so this this point I hear I'm going to shift one this is when you point this point I hear a little shift 1 2 3 that's my new point and if I do that to the left side, and over here I should do all the points 3 year surrender day okay so just read a graph is my graph for how to relax my history and in the end I do want to live with that crap at such okay we could also have graph sandwich we'll be able to magnify okay so the suit age of X is equal to 2 times out to another next to it when we do this here we're going to come up with a third column which is when I tried to do it earlier we're going to magnify time to do my outfit not shifting but we're we're increasing or decreasing by it the magnitude in which the graph goes to the right and go to the left so I'm going to start out with same except I'm going to multiply this is too. Cifelli fax okay don't want to take this out but okay and x 2. set of 2 on a 2 2 x 2 inches for all I do 1 x 2 which is 2/0 times 201 times 2 to 2:10 so I'm going to graph 42024 Wythe the negative 2 to 2 so here's my breath with this 00 still the same I'm using this cereal with visceral fat first and third column instead of one one which ones are here I'm going to end up using this one and two I'm going to bring up right one up to I'm going to use right two up for and then I'm going to keep it symmetrical outside versus my my original parent function y equals absolute value of x would have been right here it doesn't go up as but because of that too because of that too I'm actually going to I mean actually in the crap is going to go higher in a factory and then the opposite could be true if I were to what if I put a 1/2 that's about an ex what magnitude it's going to be one half with me if it's a fraction I'm not going to go as high as it hears with my excellent teacher initial he's going to look like memorize this to 2101 to buy third column I'm going to multiply this why, I'm going to multiply that by 1/2 and maybe I should put it like this because of this 32 * 1/2 is 11 * 1/2 is 1/2 0 * 1/2 * 201 * 1/2 1/2 2 * 1/2 is 1 love you traffic is in the parent function so I'm going to only graph is negative to one photograph negative 1 1/2 what about halfway been in 00 this is always my first text and then the same thing is going to be symmetrical on the right side pick this is my grand for that. 6 1/2 x the goal for this is to Cuba Libre absolute value equation and which they're going to look like this just my luck similar to the vortex one day that we've been doing so is my magnitude it lets me know how quickly you are out slowly by the valley is it going to rain and then the H in the cake is going to be like over text with a grass starts and also the middle but make sure I did negative H and K so this is the type of graph should I be able to do so let's put all this together and I know I I can't really get as deeply as I want to so Audible Justin Bieber the graph of these functions so if I have this equation hey this is Deval to be able to graph a function know what this supposed to be at the end absolute value x - 2 + 3 so if I have this what I'm going do it right I need to know first of all where is my vertex it's going to be a positive to positive 3 okay my aim is one so that means I don't have to have that. some of that shift all the points write 2 at 3 so I'm thinking about negative to negative 1 0 1 2 and I'm my output Spinners 21212 cuz of the absolute values I'm going to go ahead and grab that first and then I'm going to shift all the points on the ship all the points says 0 0 I'm going to move to write to Bright 2 3 and if I want to because they are the same I can also from here graph this shape okay write one up on right to up to left on upward until 2 I can grab that shape this would be thanks babe of the graph x - 2 + 3 okay let's see if you could do this one so let's make it slightly harder but this week is to be with a graph any of the previous problems but also I just put it all together with a with an absolute value function that shift left and right okay as well so if you like you could take press the pause button here and then see if you could do this and figure it out I'll get as far as long as you can finish it and then you could press play your note to verify your answer write the first of all we're going to get our information so this time we're going to add a magnitude is 3 is equal to 3 so I'm going to make sure I take that into account so I I know I'm supposed to create that third, negative to negative 1 0 1 a parent function is to 1012 you should be memorized by now I'm going to multiply that is 2 by 3 which makes it 6-1 * 3 is 3/0 * 3 is I'm just multiplying the second column by 301 * 33036 notice that it's symmetrical so if I wanted to I can go ahead and get one, too and then from here Lenovo right one I'm right here right one up three let me just left one up today cuz I did that one only did a 2.28 which is up  or right to up 1 2 3 4 5 6 -1 it's also  should be symmetrical so this is minecraft g of X is equal to 3 I'm checking is the vertex at 1, 2 and I want to make sure my first points I like supposed to write 1 up 1/2 that's what I'm going to be checking for make make sure that these graphs are correct 3.7 review assignment is there can you make sure you grab that your problem and please straight edge of graph paper go to graph you could always change your units if it's like a big number that you have to graph vertically like you can go each unit as you know five units so beef 10 15 20 if you put down for a half miles excetera so so you'll have these screencast notes for Pleasant Hill through Tuesday you'll have the 3.6 in a 3.7 assignment so you're turning those four things for this week for the assignment packet by Friday 3 p.m. now you can start turning turning it in today obviously if you start finishing right have a wonderful day don't forget to turn in the notes along with the assignments and I will see you all on Monday for gym class have a wonderful day

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Algebra 1 3.7 Review Notes

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