 In this video we present the solution for question number nine for practice exam number one for math 1210 and we're asked which of the following graphs corresponds to a one to one function. So this is going to be three questions for the price of one you'll be given three graphs and you need to identify which of them are one to one functions. Now, to be a function it needs to pass the vertical line test that is, if we take any vertical lines and hit it over the domain, it needs to hit the graph only in one location. In which we see all three of these are in fact going to be functions, right? So the thing to watch out for would be something like the following of course. Let's say that your, here's your x and y axis, if you had some type of function or I should say some type of graph that maybe looks something like this, you'll see that this function does fail the vertical line test. It's not going to be a function. So to be a one to one function you first of all have to be a function. It's important to pass the vertical line test, but what does one to one here mean? It means it needs to pass the horizontal line test. So if we start hitting the graph with horizontal lines that needs to hit the graph only in one point. So this tells us that the first graph is in fact a one to one function. With the second graph we see no horizontal lines hit the graph in more than one location. This fails the vertical line test. And then if we hit the graph, the third one, we're going to see it's going to pass the horizontal line test. Excuse me. The second graph, it passed the vertical line test. It failed the horizontal line test. Graph number three passes both the vertical and horizontal line test. So it is in fact a one to one function. So the correct answer would be one and three, which is option E right here. But I'm going to bring back that example I mentioned a moment ago. That's one you have to watch out for because when you look at this graph right here, this graph does pass the horizontal line test, but it doesn't pass the vertical line test. So you have to do the horizontal and vertical line test to see if the graph corresponds to a one to one function.