>> The horizontal asymptote can be identified in a couple of different ways. One way is to use a kind of a rule approach that when the numerator and denominator polynomials have the same degree, then here's what you do. They have the same degree, just look at the co-efficients of the highest degree term and then make a fraction with those co-efficients--its 12 over 3; so that's why I'm writing 12 over 3 here is equal to 4; so there is a horizontal asymptote at Y equals 4, so we come over here N at Y equals 1, 2, 3, 4 we have a horizontal asymptote. Now notice where they cross and now the behavior of the graph is fairly sort of pre-determined here in that the graphs, I say graphs, it will have a couple of branches here, but the graph will get infinitely close to these asymptote lines at the extreme to the coordinate plane. Now what is left for us to do is discover whether or not the graph kind of makes a curve here, makes a curve here, makes a curve here or makes a curve here. We can discover that by just plotting a couple of points. It doesn't take very many of them and it turns out that this one I believe has a behavior something like this. But the important thing is to identify those asymptotes as kind of the first order of business. Now let's come back over here. I want to explore this a little further. I mentioned that there were a couple of ways of discovering the horizontal asymptote; and this is one way, kind of a rule approach; and another way is by thinking about what happens when X values get incredibly big or incredibly big negatively. And we can do that here. We can say well gee if X is a 1,000 then the number in the numerator would be 12,008; about 12,000. And in the denominator if X is 1,000 we have 3,000 minus 9--about 3,000 you see so this number is about 12,000. That number is about 3,000 so dividing we get about 4,000 you see so or excuse me about 4, and therefore the graph is going to get really close to 4. It's never going to get exactly 4; we can't make this fraction exactly 4 no matter how large the value of X is. It can be 10 million you see times 12 and 10 million times 3; still this fraction will be about 4. Alright so that's a way of identifying the position of that asymptote.