in this video we're going to talk about how to tell if a graph represents a function using the vertical line test so let's start with a linear function y equals x and this function looks like this is basically a straight line so now we need to do is draw a vertical line notice that the function touches the vertical line only at one point so that means this graph is a function now let's try another example so this graph is associated with the equation x is equal to y squared is it a function now if we draw a vertical line notice that it touches the line more than one point it touches out two points so therefore this is not a function it doesn't pass the vertical line test now here's another example for you so let's say if we have a parabola this is y is equal to x squared is it a function what would you say well let's see if it passes the vertical line test notice that it touched it only at one point so this passes the vertical line test now what if we have a circle let's say the equation is x squared plus y squared is equal to nine is it a function well we can clearly see that it's not going to be a function it touches the vertical line at two points so therefore that's not a function now what about this equation y equals three does it pass the vertical line test y equals three is a horizontal line and so if we draw a vertical line it's going to pass the vertical line test it touched it only at one point but now what about x equals four will that pass the vertical line test so x equals four is a vertical line and if you draw a vertical line on it it's going to touch it at an infinite number of points so that's not going to be a function now what about these two graphs let's say the square root of x and also the absolute value of x go ahead and try these two determine if they're functions or not so the square root of x looks like this and the absolute value function is like a v shape so this one passes the vertical line test and so there's this one so they both represent functions here's another two examples that you could try try that one and also this one on the right this is the graph for sine x so looking at the first one we can clearly see that it does not pass the vertical line test it touches it at least three points for that particular vertical line now the sine function is a function and it passes the vertical line test but this one does not now what about this function x cubed and also the cube root of x now the fact that i call it a function indicates that it's probably going to pass the vertical line test so x cubed looks like this and the cube root of x looks like that and both of them are functions as you can see they pass the vertical line test and let's consider one more example so is this graph a function well we can see that it does not pass the vertical line test it touches at two points so now you know how to tell if a function or if a graph represents a function using the vertical line test you