 So before we consider the graph of a rational function, it's useful to also consider these signs and magnitudes, and so it's helpful to introduce two more sign-in-magnitude situations. First of all, a number close to zero is a small number, so there's our magnitude, and so a number divided by a small number. Well, if I'm dividing by a small number, what I end up with is a large number. If I take a small number and divide it by a number, I end up with a small number, and those are the magnitude situations, and the signs are going to follow exactly the way that they do normally. So if I have a positive number close to zero, well, that's a small, small positive number. If I have a number divided by a small number, that's going to be positive or negative depending on the signs of the numbers involved. So, for example, let's determine the sign-in-magnitude of the expression 3 over x plus 5, if x is slightly less than negative 5, and if x is slightly more than negative 5. So it's helpful to draw a number line in this situation. So if x is slightly less than negative 5, so x is over here someplace, then x plus 5, this denominator, slightly less than 5, I'm going to add 5, and I'm going to end up over here, and that's going to be close to zero, but it's slightly negative. So it's going to be a small negative number, and my quotient 3 over a small negative number is going to be a large negative number. So we might summarize this. If x is slightly less than negative 5, 3 over x plus 5 is going to be a large negative number. If x is a little bit more than negative 5, so I'm a little bit to the right of negative 5, then I add 5, then x plus 5 is going to be a small positive number. It'll be close to zero, but it'll be positive. So that's a small positive number. So when I divide 3 divided by x plus 5, that's 3 divided by a small positive number, that's going to give me a large positive number, and so if x is slightly more than negative 5, 3 over x plus 5 will be a large positive number.