 In this video I'm going to talk about compressing horizontal, so what I'm going to do is I'm going to take a function, so we have a little function here, and we're going to compress this thing horizontally. We're going to perform a horizontal compression of this function by a factor of one-half, so we're going to take this and kind of reduce it by one-half, but we're only going to reduce it horizontally by one-half. Okay, now with any sort of function, if I want to do any sort of compressing or stretching or translating or anything like that, I need to have a couple of points. So a couple of points that I'm going to use is zero negative two, I'm also going to use this point here, which is one-zero, and I'm also going to use this point, let's see this is a good point over here, which is three-two, okay, so there's a couple of points I'm going to use. Now what I'm going to do is I'm going to horizontally compress this function, and what I'm going to do is I'm going to take the points here, these three points, and I'm going to horizontally compress them so that when I horizontally compress them, basically what's going to happen is everything's going to get a little bit smaller, everything's going to get a little bit closer together. So basically what's going to happen is I'm going to take these points and I'm going to modify them somehow. Now how am I going to modify them? Well this is horizontal compression, when we talk about the horizon, we talk about the x-axis, and that's telling us we're going to do something with our x-coordinates, horizontal x-axis, x-coordinates, okay, so we're going to take these x-coordinates, the three, the zero, and the negative one, and we're going to compress them by a factor of one-half. So we're actually going to take this point, three-two, and we're going to compress it by one-half, we're going to compress it by one-half. Now notice we're only going to change the x-coordinates, again horizontal compression, horizontal, which is left and right, which is the x-axis, which is my x-coordinate, so I'm only going to affect my x-coordinates by a factor of one-half, I'm going to multiply them by one-half. That's going to change this to one-point-five-two, so this half of three is one-and-a-half. So that's my new point that I'm going to use, okay, so zero negative two is my next point, what I'm going to do is I'm going to compress this by one-half, which is nice because zero times one-half doesn't change anything at all, so that point actually, that point there actually stays the same as zero negative two, kind of nice, okay, and then this one over here, the last one is negative one-zero, okay, so if I compress that by one-half, I'm going to multiply by one-half, multiply one by one-half, excuse me, zero there, and what's going to happen is half of negative one is a negative point five, negative point five, okay, now notice that the y-coordinates didn't change at all, y-coordinates didn't change, it's only the x-coordinates because this is a horizontal compression, horizontal, which is your x-axis, which is your x-coordinates, so we're only affecting the x-coordinates, so now I'm going to take these new points, I'm going to put them on the graph and see what this looks like when I compress this horizontally, all right, so one point five, so one and then point five and then two, one, two, okay, all right, then we also have zero, zero negative two, so it looks like that one stays right there, and then we also have negative one-half zero, so that's my new point right there, okay, so it looks like my new function is going to look a little bit like this, straight line there, and a curve there, all right, so that's what it looks like, and we can tell, we can tell that this has been compressed, we are squeezing in, squeezing in, squeezing in this function, okay, so that's one way to compress horizontal, we are squeezing, squeezing in this function, okay, and by squeezing in the function, in general, what have we done? We have taken the x, y-coordinates, we have modified them somehow, but in this case we have only, we have only, let's use a variable, we've only affected the x-coordinates, we've only affected the x-coordinates by a factor of A, in this case the A is one-half, a factor of one-half, so a little bit different this time, these numbers are getting smaller instead of getting bigger as opposed to the stretching that we did in previous video, all right, so that is compressing horizontal, that is compressing horizontal, so now you can well imagine that next we have compressing vertically, compressing vertically, okay, so what we're going to do is we're actually going to make this shorter, so that's what we're doing here, we're going to make this shorter, shorter is one way we can, we can use to describe what we're about to do, so the first thing I need to do is I need a couple of points, so this point is going to be 0, negative 2, I'm going to use the same points I did last time, this is going to be 3, 2, there's another point, and then this point over here is going to be negative 1, 0, negative 1, 0, all right, so we are compressing vertically, compressing vertically, now again when we think vertical, we think of the y-axis, the y-axis and the y-coordinates, so we're only going to affect the y-coordinates, so we're going to take our points, we're going to take our points and we're going to change them, but we're only going to change the y-coordinates, so notice this time that we're going to take the y-coordinate and we're going to multiply by one-half, but only the y-coordinate, only the y-coordinate, so this is going to be 3, 1, so that's going to be one of our new points. Now again, compression vertically, compression vertically, vertical is your y-axis, y-axis and the y-coordinates. So notice here, when I look at this point, I'm only changing the y-coordinate, changing the y-coordinate. So let's do that for the rest of the points. So zero, negative two is my next point. Change that to zero. The x-coordinate is going to stay the same, but I'm going to take the y-coordinate and I'm going to multiply by one half, which is going to change this to zero, negative one half. Half of negative two is negative one. Alright, last one we have is negative one zero. I'm going to modify this point by taking the y-coordinate and multiplying by one half, but again, multiplying by zero is awesome and nothing actually happens. All I still get is zero. So now these are my three new points that I'm going to use to graph to show what it looks like when I compress a function vertically. So these are my three new points. So one, two, three, one, and zero, negative one, and negative one, zero. So actually that point right there stayed the same. There's a lot of, looking through the compression, the stretching, and the horizontal and the vertical, all the different combinations, there's a lot of points that actually stay put. Kind of interesting, kind of interesting. Alright, so this is what it's going to look like. This is what it's going to look like when I compress vertically. We get shorter. So that one goes there and then this is a curve. This is a curve. So look you there. That's what it kind of looks like. That's what it kind of looks like. Everything got shorter. Everything kind of squirter. Shorters are a squat. Different ways to explain that. Okay, so that's a video on compressing horizontally and compressing vertically. One thing you got to remember, that when you compress horizontally, when you compress horizontally, you are squeezing everything together and you're just affecting the X coordinates. You're just affecting the X coordinates. And when you compress vertically, you're only affecting the Y coordinates. Only affecting the Y coordinates.