1. (12 points) (Conceptual Question; Prepare BEFORE in-class part.) Consider a rational function () where p and q are polynomials. Assume that p and q have no common zeros, i.e. there are no holes. (1.1) Explain how the multiplicity of a real zero of p(x) affects the sign line for 24). 9( (1.2) Explain how the multiplicity of a real zero of qx) affects the sign line for ) 2 + 3.1 - 28 3 + 3.2 - 9.C + 5 (1.3) Determine the zeros and asymptotes of R(2) your answers. Show your work to support Hint: Use the Rational Zero Theorem to factor the denominator. Zeros: Asymptotes: (1.4) A blank sign line for R(x) is shown in part b. Your goal is to fill it in. In part a, do the requested work. In part b, fill in the sign line and add justification. a. Test a specific value in the left-most interval to determine the sign in this interval. Show the value and the test below. b. Use (2.1) and (2.2) to determine the signs of the remaining intervals. Do not test specific values in these intervals. Under each interval, justify your answer by stating whether you used (2.1) or (2.2). Zeros/Asymptotes (Fill in the blank) 1 1 Sign (circle one) +/- +/- +/- +/- +/- Justification from part a.