Hey everyone. Now that we know what asymptotes are, we need to be able to determine where they are on our graph when given a function. So whenever I'm given a rational function, I need to be able to determine if there even is a vertical asymptote and where exactly that vertical asymptote is. Now luckily, finding vertical asymptotes is super simple and almost identical to finding the domain of our function when we set our denominator equal to 0 and solved for x. We're going to do the same thing to find vertical asymptotes, set our denominator equal to 0, and solve for x. But before we do that, we're just going to write our function in lowest terms. So we're going to do two things that we already know how to do in order to find our vertical asymptotes. So let's go ahead and walk through this. So like I said, to find our vertical asymptotes, we want to go ahead and put our function in lowest terms. So looking at the function that I have here, I have x+2 plus 2 times x minus 3. So to put this in lowest terms, I'm going to go ahead and cancel my common factors, which here is x+2. So this leaves me with the function 1x-3, and now my function is in lowest terms. Now I'm simply going to set my denominator equal to 0 and solve for x to get my vertical asymptote. So if I take x minus 3 and I set it equal to 0, I'll end up with x equals 3. And that's my vertical asymptote, and I'm done. That's all we need to do in order to find those vertical asymptotes. Let's go ahead and look at a couple more examples and find some vertical asymptotes of different functions.

So looking at my first function here I have f(x) is equal to 22x+6. So remember the first thing we want to do is write our function in lowest terms. Let's go ahead and do that here and factor. So my numerator cannot be factored; it's just a constant, it's just 2, But in my denominator, I can go ahead and pull out a greatest common factor of 2, and that leaves me with x+3 in my denominator there. So writing this in lowest terms, I'm going to go ahead and cancel these twos, leaving me with 1x+3. Now I can go ahead and set my denominator equal to 0. So setting this denominator equal to 0, isolating x, I'm just going to subtract 3 on both sides, leaving me with x is equal to negative 3. So that's my vertical asymptote of this function and I'm done.

Let's look at one more example here. Here I have f(x) is equal to 1x2-9. Now looking at this function, we want to go ahead and write it in lowest terms but because my numerator is just 1, that's not going to cancel with anything in my denominator. It's already in lowest terms. So I can just go ahead and take my denominator and set it equal to 0. Now solving for x here, I want to add 9 to both sides. Canceling that 9 out, leaving me with x2=9, And then I can go ahead and square root both sides to isolate x, leaving me with x is equal to plus or minus the square root of 9, which we know is just 3. So this tells me that I actually have two vertical asymptotes, one at x equals positive 3 and one at x equals negative 3. It's totally okay to have more than one vertical asymptote. That's going to happen sometimes, and it's perfectly fine. Now that we know how to find vertical asymptotes, let's go ahead and get some more practice.