If the graph of a rational function r has the vertical asymptote x=4 the factor x-4 must be present in the denominator of r

" We say that f(x) is in lowest terms if P(x) and Q(x) have no common factors. 1. ... The rational functionf(x) = P(x) / Q(x) in lowest terms has horizontal asymptote y = 0 if the degree of the numerator, P(x), is less than the degree of denominator, Q(x). ... For example, just because x = a is a simple root of Q(x) does not mean that it ... "