Graphically we have7 y 1 x 1 6 lastly we construct a

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Unformatted text preview: is no way any environment can support infinitely many bacteria, so shortly before t = 5 the environment would collapse. Now that we have thoroughly investigated vertical asymptotes, we now turn our attention to horizontal asymptotes. The next theorem tells us when to expect horizontal asymptotes. Theorem 4.2. Location of Horizontal Asymptotes: Suppose r is a rational function and ( x) r(x) = p(x) , where p and q are polynomial functions with leading coefficients a and b, respectively. q • If the degree of p(x) is the same as the degree of q (x), then y = of the graph of y = r(x). a b is thea horizontal asymptote • If the degree of p(x) is less than the degree of q (x), then y = 0 is the horizontal asymptote of the graph of y = r(x). • If the degree of p(x) is greater than the degree of q (x), then the graph of y = r(x) has no horizontal asymptotes. a The use of the definite article will be justified momentarily. 4.1 Introduction to Rational Functions 239 Like Theorem 4.1, Theorem 4.2 is proved using Calculus. Nevertheless, we can understand the idea x− behi...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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