 In this video I'm going to talk about identifying transformations of parent functions. So basically what we're going to be doing is we're going to look at a couple of examples of functions and we're going to compare them to their parent functions and then what we're going to do is kind of explain what the, or describe what the transformation is. Okay, so directions here. All right, so again we are identifying transformations of parent functions and again I do have a previous video on parent functions. Today we're going to identify the parent function for G. Now what does it mean when we talk about G? We're talking about this function down here labeled G and also this one labeled G. Okay, two different G functions. Okay, identify the parent function for G for its function rule. Okay, so this is the rule here. We call it rules, we call it functions, we call them equations. Call it a couple of different things, but this is a rule right here. Identify the parent function and then graph G on your calculator. So you might have to have a graphing calculator or some sort of app on either a phone or an iPad or some tablet to be able to graph equations. So we're going to graph G, this little function, on our calculator and describe what transformation of the parent function it represents. So we're going to describe how it moved, how it shaved, did it get compressed, did it get taller, did it move, did it up, down, left, right, what happened to it. Okay, and again you'll need a graphing calculator for this so you can kind of follow along. All right, so the first example, G of X is equal to X minus 3. So the first thing we want to do is identify the parent function. Now as I look at this, I notice I want to look right here at the X. This is X to the first power, X to the first power. The one is not written there, we just understand that it is there. The reason behind that is we don't want to keep writing the one there. It's a little bit redundant and we have to write it all the time. So mathematicians very long ago just decided if we put an X there we understand the exponent is 1. If we write a variable, the exponent is 1. Let's just use that and just move on with it so we don't have to write it all the time. That's basically what we use it for. Anyway, so X to the first power, so we want to identify the parent function. If this is X to the first power, this is going to be a linear function. This is going to be a straight line. Now I'm not talking straight line left or right or up and down, this is going to be kind of a diagonal line. So it's going to go up into the right or up into the left, something to that effect. That's what a linear parent function does. So that's what it is, that's what it looks like. Now this is the time where you need to get out your calculator because now what we need to do is we need to graph this. We need to graph G on your calculator and describe what the transformation of the parent function represents. So we want to graph it and see how it changes from our original parent function. Now I'm not going to switch back and forth between different programs for this video. I'm just going to give a rough drawing of what this looks like. But again what you want to do is you want to follow along with your graphing calculator. Now for most graphing calculators, I'm not familiar with them all, but for most of them what you want to do is you'll have an equation that looks something like this. Y1, this little sub one just means your first Y equation, your first graph equals X minus 3. That's what you want to plug in into your graphing calculator. If you don't know how to plug an equation into a graphing calculator, this would be a great time to find a friend who knows the graphing calculator better than you, somebody who's taken the class you're currently in, or ask your teacher, parent, something to that effect if you don't know quite how to plug in these equations. Now what we do is you plug this into your graphing calculator. Now we all at this point should know what a linear equation looks like. So over here what I'm going to do is I'm going to draw that linear equation. So here's my Y axis, here is my X axis. Now the parent function looks something like this. This is my linear function. This is my parent function. Most linear functions look like that. Now this one here, after I've plugged this into my graphing calculator, this is what it looks like. 1, 2, 3. You know what, let me get a different color. Let me try some little different colors so we don't get confused on the colors. A lot of times when you look at equations, when you look at graphs, if they're of the same color, it's the same function, that's all I want to confuse us. So let's do a little bit different. Let's do red. So this is my G of X. This one here, this is G. The red one is G. So then when you graph it, after you're graphing your graphing calculator, that's what it looks like. So describe what has happened. That's what we're supposed to do. Describe what transformation of the parent function it represents. Describe what happened. Well, what happened, it looks like, so here's the original parent function. It looks like we brought everything down three units. And there's where G of X is. There's the new rule. There's my new function. So notice what we have over here. X minus 3. Look at what that negative 3 did. It brought the parent function down three units. So that's what I'm going to describe. I'm going to say moved down three units. And that's it. This is a linear function. And how is it moved from the parent function? It has moved down three units. That's it. So I need to identify the parent function and then describe what the transformation is. Now, I need a graphing calculator for this because I need to know what the G function, I needed to know what this looked like when I graphed it. All right, so now I'm going to go on to the next example. Go on to the next example. G of X is equal to the quantity X minus 2 squared plus 1. So now when I look at this function, it looks a little bit complicated. There's a lot of stuff going on. I'm squaring this quantity. I might have to foil this plus 1. A lot of stuff going on. If I want to identify the parent function, it's very simple. Find the variable. So here's the variable here. And what power is the variable going to be? That's what you need to ask yourself. Just like up here, for the first example, it was X to the first power. So it's a linear function. So now I got to look at this variable, X to the what power. Now, since there's no power here, we're going to look at it as if it's a 1. But this X is being squared over here. So actually this squared is going to apply itself to the X, which means this function is going to be X to the second power, which means from our parent function, this is going to be a quadratic function. So that's what the parent function is. It's quadratic. So now if you remember your quadratic function, this is going to look like a bull or a smiley face or whatever you want to look at. It's what we call a parabolic curve. So now again, this is the point where you need to plug this function into your calculator to see what it looks like. Now what I'm going to do, kind of similar to last time, is I'm going to graph the parent function, and we're going to compare it to what it was. I need a little bit more room here. Need a little bit more room, so let me get rid of this old stuff. Get rid of the old stuff. Actually, you know what's great about computers is I can take this old stuff. And I can move it. Oh, isn't that cool? Isn't that sweet? I love that. I love this about computers. All right, here we go. All right, so what I'm going to do is I'm going to graph the parent quadratic function. So here's my y-axis. Here is my x-axis. And my parent function looks like this. It looks like a smiley face. Curves up here. Curves up here. It looks like a happy old graph. It just looks just like that. So now what I'm going to do is I'm going to plug this in to my graphing calculator, and again, it's going to look something like this. y1 equals... Now, this is where you need to know a little bit about your graphing calculator. You're going to have parentheses, x minus 2. Now, depending on some calculator, sometimes you're going to have a squared up here. Some calculators allow you to do that. Now, there's other calculators, depending on what you're using. Some of them will make you use the carat button. The carat button is it looks like an up arrow. This means exponent. It means take this quantity to the second power. That's what this little carat means, and then you'll have a plus 1 after that. So this is what it's going to look like when you plug it into your calculator. Some calculators will allow you to do the squared, and you'll have just a little squared button up here. Depends on your calculator. Depends on what you're using. But again, highly suggest that you either talk to your teacher or talk to somebody who knows how to use this so you know how to graph these. All right, now, once you've plugged that in, once you've plugged that in, I'm going to change my color here, and what's it going to look like when you plug that in? What's it going to look like when you plug that in? And after you've plugged it in, what happens is it shifts to the right and then up. Notice my smiley face has now been shifted right and then up, okay? That's my smiley face now. That's where it has moved to. There's my parabolic face. There's my parabolic curve. There's my parabola. That is where it has been moved to. Okay, so now what I'm supposed to do is I'm supposed to describe this transformation. What happened? Now, if you look at your graph, you can kind of be a little bit more exact with this. It moved two to the right and then one up. Notice these numbers over here. Two to the right and then one up. Okay, two to the right and then one up, okay? Later on, we're going to go into a little bit more detail about why this is, why this negative two moves to the right and why this positive one moves one up. We're going to go a little more detail, but for right now, we're just using a graphing calculator to do this. So that's exactly what I'm going to say. I'm going to say moved. I have a lot of room here. Moved two units, units right and one unit up. Two units to the right and one unit up. A lot of stuff going on here. A lot of stuff going on here. So that's identifying transformations of parent functions. Those are just a couple of examples. Now again, you're going to have to have a graphing calculator when you do this so you can compare your old pictures. So your old parent functions with the new pictures. Your old parent functions with the new, with the new G function with the new rules. So you're going to have to have an idea of what the parent functions look like and you're going to need to be able to graph them to see what the new ones look like.