 In this video, I'm going to talk about the vertical line test. This is a test to determine. It's a very simple, very visual way of determining if a graph of a function, or, excuse me, if a graph is a function. OK, so we're going to use the vertical line test to determine whether each relation, here we go. Sorry, over again, use the vertical line test to determine whether each relation is a function. If not, identify two points a vertical line would pass through, OK? So if not, give me evidence of why it is not a function. OK, so we're going to get this graph down here. For those of us who don't know, this is a sine graph. Now, depending on your level of mathematics, you might not know what a sine graph is, but that's OK. This is a good example for our vertical line test. So notice that the graph starts over here, and just goes up, and down, and up, and down, and up, and down, crossing over the x-axis. So it looks like it goes up the same distance that it goes down, all things like that. But the vertical line test is actually relatively simple. What you simply need to do is, now, usually on a piece of paper, something like that, you will have, let me get this out, usually on a piece of paper, you will have, I like to use a ruler when I do this, but since I'm doing this on the computer, I will use a little bit of technology here, here we go. OK, so for the vertical line test, what you want to do is you want to have yourself a vertical line, trying to make this as vertical as possible on this, see if I can make that as vertical as possible, there you go. And now, with this vertical line, what I'm going to do is I'm going to pass over the graph, I'm going to pass over this graph, and see if the vertical line is going to intercept the graph at two separate points. So I identified two points that a vertical line would pass through, that's kind of what we're looking for. We're trying to pass this line over this graph and see if it hits two points. OK, so as I start here on the right side, so the line is intercepting at one point, intercepting at one point, notice we're down here now, intercepting at one point, down here, still intercepting at one point, keep going, keep going. And you see the graph is only hitting at one point. It doesn't matter how far we go, we still just intercept it, just this one point. So we're intercepting one point right here, one point right here, as I keep moving, intercepting one point here, right here at the tip top, still just only intercepting at one point. So it looks like, doesn't matter where I put this vertical line, it looks like I don't intercept at two different points. Now since I don't intercept at two different points, this is what we would call, this is a function. So this is an example of what a function is. Now again, we don't have any equations, we don't have any real numbers. I mean yes, there are numbers on our graph for our X's and for our Y's, but we really have no numbers to work with, we just have pictures, we just have lines, we have curves to work with. And so that's the basics behind the vertical line test. Now I do have another example, I think. Oh, there it is. Okay, must have went past it too much. Okay, so this is the vertical line test, this is another example of that. So what I'm gonna do is I'm gonna grab, I'm gonna create my vertical line once more, I'm gonna create my vertical line once more, so I get it as vertical as possible. Now this is much, much easier to do in real life rather than be on a computer to try to do this. I usually just grab a ruler, user pencil, whatever it is that you have at the time. So again, use the vertical line test to determine whether each relation is a function. So notice here we got a graph. Now you might look at this and think, okay, those are two separate lines. But notice the color of them, this one is red, and then this one here is red. This is actually one function. This is one way that your books or your authors, depending on who it is, when they do problems like this, when they create problems like this, they usually use the same color to represent a single function. So notice it's red here, and then we also got red here. So this is actually only a single function. And so if I grab my vertical line and try to see if the vertical line passes through two points, notice that as soon as I put it on the graph, there's two points. There's one point right there, one point down right here. So as I keep moving my line, one point right there, and another point just right there. Keep moving my line up here, one point here, one point there. Doesn't matter where I move it, I intercept twice. Those two intersections make this not a function. This is not a function. Again, if we intercepted two different points on this graph, that is not gonna be a function. So there's a couple of different examples of using the vertical line test. Very, very easy test to use. All you gotta do is use a ruler, use a pencil, something that is straight. You put it vertical on the graph. If it intersects at one point, it is a function. If it intersects at two points, it is not a function. That's the basics behind the vertical line test. That's a little summary of our vertical line test. Okay, that's it for this video. I hope this video was helpful.