 In this video, I'm going to talk about evaluating different functions. In this video, we're going to concentrate a little bit more on, this is just an introduction to function notation, okay? So we're going to evaluate a couple of functions, I have one function here, this is one example, this is actually using function notation as we can see here and then I have a separate example off here to the side, that's just a picture, it's a more visual example of this, okay? So we're going to be evaluating functions. For each function, evaluate f of zero, f of one half, there's supposed to be a bar there, f of one half and f of negative two, okay? So basically, what function notation is designed for is to very easily figure out your inputs and your outputs, okay? Now this is the notation that we use, these are the symbols and the language and the symbols and language and the letters that we use to tell us, okay, what we want to do is in a certain function and this function is called f, we want to plug in the number zero and this function f, we want to plug in the number one half and the function we want to plug in negative two. So notice over here, this function has an x in it where these other ones have a zero. So basically what I want to do is I want to take this function, I want to take this and I want to plug in these different numbers, that's it, that's basically all it means. So I want to take the function and I want to plug in zero to it, so I'm going to use this first one, I'm going to evaluate f of zero, f of zero, okay? Basically what that means is I'm going to take zero and instead of plugging in an x, I'm going to plug in a zero, okay? So in my equation in this side over here, instead of an x, what I'm going to do is I'm going to plug in a zero. So this is going to be eight plus four times zero, replacing the x with a zero just like replacing this x with a zero, okay? Very, very basic concept of, okay, how do we use notation to say, okay, plug in these numbers? That's basically what this means, okay? So after eight plus zero, or eight plus four times zero, four times zero, zero plus eight is just going to be eight, okay? Very simple, not too, not too terribly bad there. Okay, we're just evaluating, we're just figuring this out, plugging in the numbers and seeing what we come up with, okay? So the same thing with f of one-half, f of one-half. So again, in this case, we're going to instead of, oops, excuse me, instead of, there's the undo, instead of plugging in a zero, what we're going to do is we're going to plug in a one-half, so four times one-half, okay? And I might need, I'm going to have to write down a little bit extra here, okay? Four times a half, or you could say to yourself half of four is going to be two. So this is eight plus two, which is equal to ten. So again, all this really means is in the function f, so this function, we're going to plug in one-half. So instead of plugging in x, we plug in one-half. So again, instead of plugging in x, we're plugging in one-half, all right? Do it for the next one, our next one is f of negative two. f of negative two equals eight plus four times a negative two, careful with those negatives. This is going to be eight minus eight, four times negative two is a negative eight, which is going to be zero, all righty. So that is evaluating using function notation, evaluating f of zero, f of one-half and f of negative two, okay? All right, now for the second one over here for this graph here, I'm going to change colors just a little bit. And we're going to look at, visualize what we're doing here. Instead of looking at just numbers, instead of just plugging in numbers, now we're actually going to visualize it, looking at a graph, looking at a picture, okay? So it's basically going to be the same thing, f of zero, okay? But you're asking yourself, where do I plug in the zero? There's no equation, there's no anything here to plug into. What am I talking about? There's no x's, there's no numbers to plug in. What am I supposed to do here, okay? Well, what you're doing is, okay, so instead of an x, what you're doing is you're plugging in a zero. So what we're going to do is, we're actually going to go to the x-axis, okay? We're plugging in x's, so we're going to go to the x-axis. So we're going to go to x-axis of zero. Zero is right here, it's right in the middle. And now what we're going to do is, when we go to the middle, we're going to find where the graph is, it's right here. That right there is f of zero. If I plug in zero for x, there's where the graph is, it's right up here. So f of zero, now what I'm going to do is I'm going to plug in the y-coordinate. This y-coordinate here, if you can't count this, is one, two, three. So my f of zero, when I plug in a zero for x, my y-coordinate is going to be three. So again, this is a more visual way of looking at function notation. Now, probably something I should have mentioned at the very beginning, if we look over here, something that you're a little bit more used to is instead of looking at this as function notation, if you look at this as an equation, as y equals eight plus four x, make that eight a little bit better, y equals eight plus four x. This f of x, all it really means, you can think of it as just your y, your y-variable, or your y-coordinate. That's one way to look at it. So that's what we're doing over here. If you plug in x, if you plug in x of zero, your y-coordinate is going to be three. That's one way of looking at this. So let's look at the rest of them. f of 1 half, f of 1 half. So now I'm going to plug in an x, I'm going to plug in an x of 1 half, plugging inputs, inputs, plugging in, an x of 1 half. So as I go here, so here's zero, here's x of 1, x of 2, x of 3. So x of 1 half is actually going to be right here, which coincidentally is where the graph is also. So actually, f of 1 half is going to be zero. I'm looking for the y-coordinate. The graph, the y-coordinate, is sitting right there at zero. It's not anywhere, it's not up, it's not down, it's just right there. So that right there, at this point right here, is f of 1 half. And last but not least, we have f of negative 2. So we're plugging in an x of negative 2. So going over here, negative 1, negative 2. This is negative 2 right here. And now what I'm going to do is I have to go up, I have to find out where the graph is, it's up over here. So an x of negative 2, and then I go up right here. This is f of negative 2 right here at this point, which is 1, 2, 3, 4. It's a y of 4. It has a y-coordinate of 4. So you can look at these as coordinates, you can look at these as function notation. There's a lot of different ways to look at this. But these are two different examples. One is with numbers, again, using function notation. So I'm plugging in, I'm evaluating different numbers. I'm plugging in different numbers. So instead of an x, I'm plugging in a 0. Instead of an x, I'm plugging in a 1 half. Instead of an x, I'm plugging in negative 2. Same thing over here. Instead of an x, what I'm doing is I'm plugging in 0. But when I plug in 0, I've got to find the y-coordinate. So there's f of 0. When I plug in 1 half, my y-coordinate was 0. Excuse me, I think I messed that up. Let me go over that again. So f of 0, f of 0 is equal to 3. So when I plug in an x of 0, my y-coordinate is 3. When I plug in an x of 1 half, my y-coordinate is 0. And when I plug in an x of negative 2, my y-coordinate is 4. That's a little bit more visual way to see that. All right, that is evaluating different functions. Two different ways to look at it. You can look at it with actual numbers and equations and notation and all that. This is one example. And then we have a separate example, which is more of a visual way to see this using lines and functions and looking at graphs and coordinates. A couple different ways to look at it. OK, that is evaluating different functions, again, either with numbers or visually. All right, that is evaluating functions. And I hope this video was helpful to you.