 In this video I'm going to talk about identifying parent functions to model data sets okay So again identifying parent functions to model data sets basically what we're going to be doing in this video is taking a data Set taking some coordinates plotting them and then seeing what turns up What what kind of what kind of parent function does this look like is it going to be is it going to be a cubic function? Is it going to be a constant? Is it going to be a linear function? Is it I mean there's a bunch of different parent functions that we have okay? So we're going to see we're going to graph this we're going to see what it looks like so again graph the data set Which we have down here from the set of ordered pairs Describe the parent function and the transformation that best approximate the data set so not only are we going to identify The parent function itself. We're going to identify how it looks differently from the original parent function Okay, so we'll take a look that here in just a second Okay So the first thing I need to do is I need to graph the data set not to not too troublesome now as I look at this data set I like when I look at some of my bigger numbers, so two negative 12 or excuse me negative 212 and then 212 12 is kind of a big number and as I look at my graph here I Don't have a lot of space So this is what I'm going to do. I'm going to change the I'm going to change the The number that my graph goes up and down by now I'm going to do that not for the x coordinates But I'm going to do that for the y coordinates so on my y-axis I'm going to go up and down by twos or threes or fours or something like that Okay, now as I see here, I have one two three four five Okay, so I might want if I go by twos it'd be two four six eight ten which still doesn't get me to twelve So instead I'm going to go by three so three six nine 12 15 okay, so that will actually get me so I can actually graph this to 12 here So again, I'm gonna go by three, so I got three six nine 12 and then that's that's it I'm not going to change my x-axis because I'm with my x is I'm going negative two negative one zero one two So I'm there's no need for me to change the x-axis only the y-axis has given me trouble Okay, so I'm going to graph this there's gonna be negative two and then 12 which is all the way up here And then I'm going to have negative one three so negative one three right here Kind of get in the way of the three there zero zero right there at the origin Right there at the origin one three so one one two Oh gotta be careful gotta be careful if I change the increments I don't I go up by threes not up by ones almost made that mistake and then I got two twelve So one two and then one two three four five six seventy nine ten eleven twelve It's handy to put those numbers right there on the side so you can see them as you're graphing All right, so now As I look at this as I look at this what what parent function does that look like well We're gonna have to connect the dots before we can see that so we start at zero zero. I'm gonna come up here The arrow I'm gonna start my zero zero. I'm gonna come up here with my arrow as I look at that That looks like a curve that looks like a smiley face So that's gonna be a quadratic function. Okay, so again, I want to describe the parent function So I've already done that. This is gonna be quadratic quadratic Looks like a quadratic function where everything's curving up into kind of a smiley face and now what I want to do is I want to and then also describe the transformation the best approximate the data set well Basically what that saying is how how is it different from the original parent function? How is it different from the original quadratic? Well, what we would need to do is we need to graph the original to see kind of how they differ like is it and Especially with changing our increments right here is it has this has it's gotten bigger smaller scrunched Widen's like what what is that? What has done what has been done to this? So what we're gonna do is I'm gonna graph the parent function on this other side here Let me use a different color Okay, so I'm gonna graph the parent function now This is where a good knowledge of the parent function. This is where the knowing the coordinates is to be really really handy For the for the parent function, I'm gonna write this in red I'm just gonna write the coordinates over here if I if I plug in a negative two So I'm kind of gonna plug in the same x coordinates if I plug in a negative two into my original parent function Which is just x squared if I plug in a negative two that's gonna give me four if I plug in a negative one That's gonna give me one Okay, so if I again if I plug in negative two negative two squared is four I plug in a negative one negative one squared is one If I plug in a zero zero squared is zero if I plug in a if I plug in a one One squared is one and if I plug in a two two squared is four So what I just very quickly did is came up with a bunch of coordinates that are gonna be used to graph this So now I'm gonna graph those real quick So negative two and then four which is about right here Okay, three four remember my increments are different and then negative one negative one which is about right here Zero zero which is right there. Well, so it looks like that they showed that coordinate and then I'm gonna have one one So one one and I'm gonna have two four so one two one two three four right about there Now I'm gonna draw this in red Okay, so the blue one the blue one is the data the red one is my parent So this is the parent this is the parent and if you can't keep track of either of them You might want to do what I'm doing here. You might want to write You might want to write what they are so that there's the parent one and this one's gonna be the data This one's gonna be the data Okay, so now now we can more accurately now that we actually see it now we can actually say okay describe the transformation Describe the transformation. Okay. Well, what I'm gonna say is Well, it looks like it got looks like it got a lot taller or you could also say everything's been compressed everything all the Everything's been kind of compressed in so there's two ways you can describe this you can say it either got taller Which now if we get to the technical terminology if you make something taller You are vertically stretching it vertical stretch or you could also say well Everything came in it kind of compressed everything you could also say this is a horizontal compression. So there's actually two There's actually two descriptions. We could have for this and either one of them would be correct Either one of them would be correct We you could either say what I say vertical stretch. I could say vertical Vertical stretch or you could also say this could be a separate this one would also be valid you could also say horizontal horizontal I Forgot my can't spell horizontal correctly horizontal There we go horizontal compression Horizontal compression. Okay, so there's two ways you could have described this and again either one of those would be correct now as I look at my points There's one of them without I would use above the other Okay, so now look at if you look at the points themselves notice that here. Okay. Here's the red Here's the parent function Everything went up this point went up this point stayed there this This point here went up this point here went up that would lead one to believe that actually a vertical stretch This thing was stretched vertically up that might be a better description of what kind of transformation this was now Again depending depending on how picky your your your instructor wants to be It doesn't really I would think it doesn't really matter which which one you used to describe it But I think both of them are valid But if you really want to be picky it looks like these points went up points went up if the points go up like that It would be a vertical stretch so a vertical stretch may be a better description of what happened but I would also say the horizontal compression still has a good argument also because Everything everything came in came in to get kind of a narrower type of graph All right, that's a that's a quick video quick example of using a data set to kind of model a parent function Identifying the parent function and then identifying the transformation describing the parent transformation from the parent function to the data set