Letr(x) = P(x) 9(2) where p & q are polynomials of degree n& m, respectively. We can express p and q as: p(x) = 2,2" + A

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Letr X P X 9 2 Where P Q Are Polynomials Of Degree N M Respectively We Can Express P And Q As P X 2 2 A 1 (58.95 KiB) Viewed 17 times

Letr(x) = P(x) 9(2) where p & q are polynomials of degree n& m, respectively. We can express p and q as: p(x) = 2,2" + An-12"-1 +...+ ao and g(x) = bmx" + bm-12-1 + +bo where (1). all aj, b, are constants, (i). m, n > 0 are constant integers, and (ii). an, bm +0. Justify your answers, (a.) (1 point) Assume p and q have no common factors. Where do the vertical asymptotes of r(2) occur? Explain in terms of p(x) and/or g(x). (b.) (1 point) As x +- (or x + o), what term dominates the behavior of p(x)? (c.) (1 point) As 2 →- (or 3 + 0), what term dominates the behavior of g(x)? (d.) (1 point) Under what condition does r(3) have no horizontal asymptote? (e.) (1 point) Under what conditions does r(a) have a horizontal asymptote at y = 0? (f) (2 points) Under what condition does r(2) have a horizontal asymptote at y = c, where c0? What is the value of c in this case?