only letter e for both questions!

MHF4U Unit 2 - Rational Funct COMMUNICATION & THINKING /Level Please complete part .... . ....... from each question. Level 1 Level 2 Level 3 Level 4 (limited some (considerable (high degree effectiveness) effectiveness) effectiveness) of effectiveness) TIPS - Use of planning skills - understanding the problem and making a plan for solving the problem including the necessary steps - Including all of the needed elements in the solution TIPS - Use of processing skills - carrying out a plan (e.g., solving, inferring, forming conclusions) - looking back at the solution (e.g., reasoning, justifying, proving, reflecting) - Performing the calculations correctly TIPS - Use of critical/creative thinking processes (e.g., problem solving, inquiry) - Interpreting the results correctly COMM - Expression and organization of mathematical thinking (e.g., clarity of expression, logical organization) COMM- Use of correct conventions, vocabulary, and terminology of the discipline (e.g., terms, symbols) 1. For the given rational function, determine the key characteristics (intercepts, asymptotes, behavior around the asymptotes) and sketch the graph of the function. Label all asymptotes and intercepts on the graph and show all of your work. a)f (x) = 3x2-12x b ) f ( x ) = * + 2 x e)f(x) =*+x-6 x2 - 2x-3 -4x+8 c ) f (x ) = x-4 d) f (x) = *-4x x 2 - 4x -5 2 x + 6 x2-25 2. Determine an equation of a rational function with the given characteristics. Explain your reasoning justify your solution. a. No x-intercepts, two vertical asymptotes, and y-int = 10. b. Two x-intercepts, no vertical asymptotes, y-int = - 6. c. One x-intercepts, oblique asymptote and vertical asymptotes at x=-3 and x=2. d. X-int=-4, y-int= - 8, and vertical asymptote x=3. e. Horizontal asymptote a y=3, vertical asymptote x=5, x-int=1