In this exercise, we want to know which graphs represent one-to-one functions. To test to see if a graph is a one-to-one function, we first have to see if the graph is a function, and then test to see if it's a one-to-one function. Graphically, the vertical line test can be used to see if a graph represents a function. To perform the vertical line test, we pass a vertical line across the graph, and if it does not intersect the graph in more than one point, it passes the vertical line test and is a function.
Once we know a graph is a function, we can test to see if it's a one-to-one function using the horizontal line test. It's a similar test, but we use a horizontal line instead. To see if the graph of a function is one-to-one, we pass a horizontal line across the graph.
And if it does not intersect the graph in more than one point, then it passes the horizontal line test and is a one-to-one function. So we always want to perform the vertical line test first, and then the horizontal line test. If the graph does not represent a function, it cannot be a one-to-one function. So looking at our first example here, let's perform the vertical line test.
So I'll sketch several vertical lines across the graph. We can see these lines would never intersect the graph in more than one point, which means this blue graph is a function. So it is a function. So now we can test to see if it's a one-to-one function.
by performing the horizontal line test. Now we'll sketch several horizontal lines across this graph. We can quickly see these horizontal lines do intersect the graph in more than one point, therefore it fails the horizontal line test and is not a one-to-one function.
So this blue graph is a function, but it's not one-to-one. Let's look at the graph here now. Again, we'll start with the vertical line test.
Notice these vertical lines do intersect the graph in more than one point, which means this graph is not a function. And if it's not a function, it obviously can't be a one-to-one function. So these first two graphs are out. Neither of them are one-to-one functions. Let's take a look at this graph here.
Again we'll start with the vertical line test. Notice these vertical lines do not intersect the graph in more than one point. Therefore it passes the function test. So we can say it's a function. And now we'll perform the horizontal line test to see if it's a one-to-one function.
Notice as we pass horizontal lines across this graph, they do not intersect the graph in more than one point. Looks like it might be close near the origin, but it does not intersect the graph in more than one point. Therefore it So it passes the horizontal line test, and this is not only a function, this is also a one-to-one function.
And then for our last graph, we'll start with the vertical line test, and again we can quickly see this fails the vertical line test because these vertical lines intersect the graph in two points, therefore it's not a function, therefore it cannot be one-to-one. So of these four graphs, The only graph that represents a one to one function is this graph here. Okay we'll look at some more examples in the next video.