>> Let's talk about several transformations all at once. This is the way that a lot of times these elementary functions can be evaluated graphically. You can just imagine the graph just by noticing things and knowing things about the possibility of transformations. Here where we have a parabolic curve. We know we have a squaring operation here, so we think about okay, this is the parabola. Now where is it located? All right. Let's decide. We start out with the idea. Our imagination is starting with a parabolic curve right here. Something like that. And then we see. Well, let's see. We see X plus 3. Adding 3 before the prevailing operation. We'll shift that graph over to the left, in a direction we don't expect, to replace this. So this vertex will go 1, 2, 3 over, and now the graph ends up here. Okay. Now, what about this minus sign? Well, the negative of this means that we are going to reflect in the X axis. So now, we think about the graph making an appearance here. And then minus 1, we'll take all of these vertical distances and move them down 1 on the coordinate plane. So the whole thing shifts down 1. This vertex goes to this point. Hey, you know, I say the vertex. It's actually all points go down. But a lot of times, a reference point is useful to notice. You choose a reference point, you move the reference point, all the other points are going to follow. You know, it's one way to look at it or to think about it very quickly. But anyway, the graph will end up in this position. You can verify this on the graph in calculator. Incidentally, the graph in calculator is very useful to experiment with these various transformations, and to familiarize yourself with them and become comfortable with them. Let's talk about the square root idea. All right. F of X is the square root of X. Here's the basic function. I want to choose this one here because I want to show that other reflection that I was talking about. If G of X is the negative of X, of the square root of X, then we're talking about the negative of all of those guys. So these vertical distances, the vertical distances described here, are just the negatives of those vertical distances. So we have this reflection in our X axis. So the reflection goes this way and the graph then looks like that. On the other hand, if we have the square root of negative X, then the reflection is in the Y axis. And so from here we're reflecting in that Y axis so the graph shifts over this way, and the graph looks like that. 

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