 In this video I'm going to talk about stretching and compressing functions, so this is kind of an example video of how to stretch or compress a function. Okay, so what we're going to do is we're going to use a table to perform a horizontal stretch of my function y equals f of x, so this is the function over here, okay, simple vertical line test tells me that yes indeed this is a function. So again we're going to use a table to perform a horizontal stretch of this function by a factor of three. Okay, now again when you look at this you might think oh I can, I might be able to do this just by looking at it, but again with a stretching and compressing you never quite want to do this just trying to put the points where they're supposed to go. You want to always try to use a table so you can get exactly what the points are supposed to do. So I'm going to start with my table, this is an x, y table, so one of the things I'm going to need to do, it's not a very horizontal line there, one of the things I need to do is I need to find some x, y coordinates on my function to help me with this. Now one of them that's obvious is right down here, okay it looks like a valley right there which is zero negative two, zero negative two, and then another one that might be useful is this one right here, this is a little elbow, so this is one two three one, so three one, and then another one over here that might be useful might be this point up here, this point up here which is negative two two, negative two two, that point might be useful. Now again depending on your function sometimes you might have two points, sometimes three, sometimes five, sometimes ten, it just kind of depends on the function. These were some important points like this was a valley, this was an elbow, this was a kind of a point that's on the arm, so I deemed those as important points that I should be able to use to modify by a factor of three. So those are important ones I thought were important anyway. So I'm going to put those points over here, so I have negative two two, I have zero negative two, and I have three one. Now this third column over here I'm going to figure out what I'm supposed to do. All right so let's think about it. I am performing a horizontal stretch, horizontal stretch. So here, horizontal is left and right, horizontal is left and right, so what I'm going to do is left and right is my x-axis. My x-axis means I affect my x-coordinate, so I'm going to do something with my x-coordinates, I'm going to stretch them by a factor of three. So I'm actually going to multiply my x-coordinates by three. So this is a little bit different from the previous videos. Previous videos, my previous example videos we just affected the y-axis, now we're actually going to affect the x-axis. Anyway, so what I'm going to do is I'm going to take these points, so three times a negative two, this gives me a new x-coordinate of negative six. Zero is my next one, so I'm going to take that, multiply by three, take the x-coordinate, multiply by three to get zero, love multiplying by zero. And then last but not least, I'm going to take the coordinate three, I'm going to multiply the x-coordinate three, multiply that times three to get nine. Pretty large, pretty large. Okay so now these are my new coordinates. Now depending on how good you are with coordinates, now notice that we have x-coordinates on the right side and y-coordinates on the left side. That's kind of confusing. If you need to rewrite the coordinates, go ahead and do that. So my new coordinate is going to be negative six, two. The x-coordinate changes but not the y-coordinate, again this is a horizontal stretch. Horizontal is left and right, which is my x-axis, which is the x-coordinates. So all I want to affect is the x-coordinates, not the y-coordinates. The y-coordinates are going to stay the same. My new one over here is going to be zero negative two, which actually looking at that is going to be the exact same point, nice. And then my new one here is going to be nine, nine is the x-coordinate and one is the y-coordinate. Nine is the x-coordinate, one is the y-coordinate. Alright so let's see if I actually have enough space on here. Let's see, do I have enough space on here? Now one of the points on here that I chose, I might not be able to put on here. So what happens? Okay so I have my first point of negative six two, so one, two, three, four, five, negative six, one, two. So this point moves quite a ways over to here. I have zero negative two, which actually just stays in the same spot, we stay right there. And this point right here is nine, one, one, two, three, four, five, six, seven, eight. Maybe eight, maybe nine, maybe nine out here, something like that. And then nine, one, that's way over here, it's almost off of my video here. That was probably a bad point to use. It's probably a bad point to use. So let's try something different. That point is way off to the side, I'm not going to be able to graph it. It doesn't fit on my grid. Let's choose a different point. This happens sometimes where you choose a point, it goes off to the grid, it doesn't really work. So you've got to go back, let's find something else. Okay so what about this point right here? That's pretty much on an intersection. One right there is a negative, or excuse me, positive two, two, negative one. Two, negative one. So I'm going to take that one and I'm going to figure out two, negative one. I'm going to figure out, take it three times the X coordinates to get six. Now that is something that's actually going to be able to fit that should be able to fit on my graph. So six, negative one, six, negative one. So as I look, one, two, three, four, five, six, negative one, right there. And then see that one's on my grid, that one's on my graph, that's much, much easier to graph than this one that's way over here and off of my grid. Okay so sometimes that happens, sometimes you need to choose a new point. Okay so what's this function going to look like? So we start here, so I have my three points, one, two, and three. So we're going to start here, I have my line that goes out to this point. Okay there's my line. And then I have my curve which gets the elbow and then I have a straight line going to the right. So curve to the elbow and then a straight line going to the right. Curve to the elbow and then a straight line going to the right. Kind of hard to do that one, it's very, it's not a very big curve over there. Anyway that is, that looks to be it. That looks like I performed a horizontal stretch of this function by a factor of three. Now again a couple of things from that, make sure that you, sometimes you're going to have to rewrite those points, rewrite the new points. Sometimes when you look at these tables they can be confusing sometimes of what the new points look like. So if you rewrite out the new points, much, much easier to see and much, much easier to graph. Alright that is, that's just an example of stretching and compressing functions.