The first thing to do on this problem is to get a common denominator, so 11 -, 12 X over X. So if we thought about graphing this, we would know that we have a vertical asymptote at X = 0. We have an X intercept when that numerator is equal to 0. So we'd have an X intercept at +11 twelfths or a .11 twelfths, 0. This case we have no Y intercept because of because if we put zero in for X, we'd get a zero in the denominator and the horizontal asymptote because the degree on top and the degree on bottom are the same. It's the leading coefficients on the polynomials numerator and denominator in this case -12 So if we thought about a graph horizontal at -12 vertical at X = 0 and X intercept at 11 twelfths, this is absolutely not scale. So this one point we know we have to cross the X axis. We've got to be close to the asymptote. We've got to be close to the asymptote. We're going to cross the axis because of the multiplicity of that term. Remember, we think about that whole term being in parentheses. The multiplicity is odd. So the Y is on one side are positive, the Y is on the other half to be the opposite or negative. Now this asymptote, we need to look at its multiplicity. Its multiplicity from the X in the bottom is 1. So if the Y's on one side are positive, the Y's on the other side are negative. And so the problem says what happens when X goes to Infinity? Well, when X is going to Infinity, the Y's are going to -12. When X goes to negative Infinity, the Y's are also going to -12. Now, another way to look at this, a different way to think about it is when X is getting really, really, really big. What's happening to this 11 / X? If we left it written as the original equation? Well, when X gets really, really big, 11 / 1011 / 111 / 1000, that's getting really, really small. So we'd end up with 0 - 12, zero -12 is -12 if we had 11 over something really, really big that was negative -100 negative 1000 negative a million, that's still going to zero, 0 - 12. The personal reason that I like the graphing is that we could ask lots of other questions off of the graph. If I had said what's the limit as X goes to zero from the right of F of X, you can easily look at the graph and tell me that that's going to go out to Infinity.