 In this video I'm going to talk about graphing functions. As you can see by this first example there are no equations, there is no function notation but what we do have here is do we do have a line of coordinates. So now functions, there's different ways to represent functions. One of them is to represent them just with data. Now if you're in a science class or in chemistry or out in real life, biology, whatever it is, it could be business, it could be money, it could be something else. You're always going to deal with data, you're always going to deal with sets of numbers. So this is a very, very basic way of introducing to you sets of numbers that are also functions and how to graph them. So in this case, I'm going to graph this function. This function is 0, 4, 1, 5, 2, 6, 3, 7 and 4, 8. So as I look at my graph I notice that these numbers are a little bit small. I know that I'm going to have to go up to 4, 8. So I know I can go 1, 2, 3, 4 out here, excuse me, 1, 2, 3, 4 but then I can't go up 8. So one thing I'm going to do is I'm going to change my increments. Instead of going by 1s, I'm going to go by 2s. So what I'm going to do is right here, I'm going to make sure that I make a notation that everything, my y-axis and then my x-axis are going by 2s and we're not going by 1s anymore. Hey, hopefully this will make it a little bit easier to graph. Okay, so first one is 0, 4, 0 for the x-coordinate, 4 for the y-coordinate. So 0, 4 is going to be right about there, 0, 4. There's my first coordinate. Okay, and then my second coordinate is going to be 1, 5, so 1 and then 5 which is going to be right here floating in space. That's okay. Okay, 5 is right here between 4 and 6, okay, so 1, 5. Next is 2, 6, so 1, 2, 1, 2, 3, 4, 5, 6, looks like we're getting a little bit of a line here. The rest of this looks like 3, 7, 1, 2, 3, 1, 2, 3, 4, 5, 6, 7, again, floating in space just a little bit. Again, it still looks like a line, 4, 8, 1, 2, 3, 4 and then 1, 2, 3, 4, 5, 6, 7, 8. Look at that. It does look like we have what's called a linear progression, it's a line that's going up. Now notice one thing that I haven't done yet is that I haven't actually drawn a line through this. This individual function is not a line. We do not have points in between here. These are the points. This is the data set that we have right here and it's only these points. It's nothing else. Notice that these are the only points that I'm going to graph. I'm not going to put a line between these because that line would represent that I have points up here, I would have points down here, and I would have all sorts of different points in between these points that I have graphed here. This is not what I want to represent. I only want to represent the function. This here, these points, this is my function. The graph of this function are these five points right here. That's it. That's about as simple as it gets. We don't want to draw a line with that because we don't want to represent more points. We only have five points we want to represent. That's my first example with graphing of functions. Here's my second example. This one is a little bit different. Instead of just having a set of numbers, what we have here is we have a function notation. We have an actual function. What you would commonly see or commonly refer to as a function because when you think of the word function, this little equation, something like this should pop into your head. Not usually the coordinates from that previous example, but usually this should pop into your head. Anyway, what I want to do is I want to graph this function. Using a function like this is, I'm assuming that it says you're learning about what a function is. You're far enough in your math career that you know how to graph equations, you know how to graph linear equations, you know how to graph lines. That's what we're going to do. We're going to relate this back to graphing lines. Instead of f of x, what we can do is we can rewrite this as y equals 3x minus 1. This is an equation using a y instead of function notation instead of the f of x. This might be a little bit more familiar for you to graph with. What I can do with this is this is slope-intercept form. Everything's already set up for me. The reason we call it slope-intercept form, y equals mx plus, that's kind of a horrible x there. Give me a moment. This is a slope-intercept form which is y equals mx plus b, m is your slope, and b is the y-intercept. In this case, my slope is 3 or some students like to write 3 over 1, and then my y-intercept is negative 1. What I'm going to do is I'm going to go with the y-intercepts. Here's a crash course in graphing linear equations. My y-intercept is right here at negative 1, and then I have a slope of 3 over 1. Now where did the 1 come from? Well, 3 is the whole number. I wanted to write the slope as rise over run, so I wrote it over 1 so I could see. I'm not sure how much I'm supposed to rise. This is how much I'm supposed to run. I'm going to rise 3, 1, 2, 3, I'm going to run 1. Notice I ran to the right. When I connect these two points, it's going to be a positive slope. I want a positive 3 over 1 for a slope. Let's do another point, 1, 2, 3, 1, and I'm actually going to come back down here and I'm going to go down. I can also go down with my slope, so 1, 2, 3, and 1 right here. In this case, for this example, this function represents an entire line that goes all the way through these points. I can keep going with all these points. I don't have a set number of points, so what I want to do in this case is I do want to draw a very crooked looking line that goes through all three of these points. This line represents that every point on that line is going to be a solution, every point. An infinite number of solutions to this equation. There's an infinite number of inputs and outputs for this function. That's what that line represents. In this case, for this example, we do want to draw a line between the points as opposed to the previous example where we did not want to draw a line between all the points. That is graphing functions, very basic example of graphing functions. Basically, two ways. You either graph data sets, let me go back real quick. You can either graph a data set, so you can either graph these coordinates, put them on a graph. Remember, there's no line there. Or you can graph a function, and it's just like graphing a linear equation, but make sure the points you put on there, you put a line between all those points so you know that line goes on forever. That is graphing different functions. I hope this video was helpful to you.