 In this video I'm going to talk about, in this video I'm going to talk about translations of an absolute value function. So basically what I'm going to do, similar to my previous video, I'm going to translate this function so I'm going to move it up, down, left, and right. Now what we're going to do here is we're actually going to do multiple translations. So we're going to do left and down or right and down or something to that effect. We're going to use both of them, not just one of them. Okay, so we're going to translate our basic absolute value function. So here's our very, very basic absolute value function. So that the vertex is at negative 1, negative 3. Now right there it's kind of a new word for us, vertex, and we'll go over kind of what that is here in a second. Okay, so we're going to translate it first, we're going to write the notation for it first, then we're going to grab it. Okay, then we're going to grab it. Alright, so first thing that I want to do actually to get an idea of what I'm moving around, I'm going to actually take this function and graph it first, okay. So what an absolute value function looks like, it basically looks like a V, okay, went over that in my previous video, basically it looks like a V, so I'm going to go up one over one, up one over one, up one over one, same thing on the other side, up one left one this time, up one left one, up one left one, okay. So it basically looks like a V, it's what an absolute value function looks like, alright. Now when I translate it, I want to translate as it says in the directions, translate the vertex. Now what's the vertex? Now if you remember from your geometry, vertexes of polygons, of shapes are the corners. So now when I look at this shape, the vertex is going to be the corner, basically the only corner that I have here on this shape is right down here at the bottom, where it changes from going downhill to uphill, this right here is going to be my vertex, okay. So on an absolute value function, right there is where the vertex is going to be, okay, where it changes from going downhill to uphill. Now if you've also done some studies of a parabola, parabolas are the smiley face looking shapes, the vertex is again kind of in the same spot where it's at the bottom of the smiley face for bottom of the cup, the bowl, whatever you want to call it. But anyway, back to what we're doing here, so again, what we're going to do is we're going to take this vertex and we're going to move it, so the vertex is at negative one, negative three, so actually I'm going to plot that, I'm going to get a different color here. I'm actually going to plot that right off the back, so negative one, negative three, so negative one, negative one, negative two, negative three, right down here. So that's where everything is going to move to, that's where everything is going to move to. So it looks like I'm going left one and then down three. Now that description right there can give you a big hint on what the notation is going to look like, what the actual function is going to look like. All right, so let's look at the notation first and then we'll get to the graphic, okay. What I'm going to do is I'm going to take my f of x function and I'm going to change it, I'm going to change it, so by taking the function and as I said earlier we're going to go left one and down three. So I'm going to go left one and I'm going to go down three. Okay, so notice the notation here, left, if I go left and right it's inside the parentheses with the x. So I'm going, this is left, this is left one, I know left you think of a negative number but when it's inside the parentheses like this we've got to kind of think it's opposite of what you think is what I usually just call it. So if you ever have plug in number inside of the parentheses it's opposite of what you think. So left one is going to be a plus one and then if I want to go down three it's exactly what you think on the outside we're going to go down three over here. So that's the change that I'm going to make, that's the notation right there of the change that I'm going to make. All right, now I'm going to decide a letter for my new function, for my blue one that I have here. I'm going to stick with the traditional, we'll just stick with G. G of x is going to be my new function and the new function is going to, I'm going to take the old one and I'm going to move it left one and I'm going to move it down three. Okay, so that's what it's going to look like. So then I have to take my original function, I'm going to add one directly to the x and then I'm going to subtract three on the outside. So take x plus one on the inside of the absolute value and then also minus three. So my new G of x function, I don't really have to do any simplifying is going to be absolute value x plus one, absolute value, close that up, minus three. Okay, so that is what the function is going to look like. That's what the notation looks like and that's what the function is. Okay, so now that's out of the way, now let's graph this thing. Now let's graph this thing. Now if I go, actually all these points are going to be relatively in the same position, we're just moving everything left one and down three. So then all of my points are going to be the same spot. I'm going to have a point here, I'm going to have a point here, I'm going to have a point here, I'm going to have a point here, I'm going to have a point here, there and also there. Okay, just moving everything left one and down three. Looks like I got an extra point there. Okay, left one, down three. Okay, this one here, left one, down three. Okay, this one here, left one, down three. All of them did that. This one here, left one, down three. Get this one here, left one, down three. one down three, every single point did that. And now I have my new, I have my new g of x function, my new g of x function. So this one here is g, okay, it looks like I didn't do what I was supposed to. This right here is my f function, forgot to do that, forgot to label it. Okay, so now I know the difference between my f function and my g function. So that's my new one. Okay, that's a quick video on doing what I would like to call multiple translations of an absolute value function. What I mean by multiple translations is we're moving, so we're moving left one and then down three. So I would be in multiple translations.