What happens as *x* gets larger and larger? It looks like the quotient is approaching 0, so we'll say The same will be true for any rational function where the degree of the numerator is smaller than the degree of the denominator. We know because we're dividing 1 by larger and larger things as *x* approaches infinity. If we have a rational function where the degree of *p*(*x*) is smaller than the degree of *q*(*x*), *q* will get larger "faster" than *p* will, and the fraction will approach 0. We'll talk more about this in a bit, and include more pictures, when we compare functions and their limits at infinity more generally. |