MATH 1001: Pre-Calculus Mathematics 3 14) Find an equation of a rational function f that satisfies the given conditions: |4 marks] Vertical asymptotes: x = -5,x = 2 Horizontal asymptotes: y = -2 x-intercepts: x = -6,x = 4 f(-2) = -4 Section 3.6 15) Page 241, Q. 10 [2 marks] 16) Page 241, Q. 34 [3 marks]5) Use the factor theorem to show that x - 3 is a factor of / (x) = x5 - 6x* + 11x3 - 5x2 - 4x + 3. [2 marks] 6) Page 199, Q. 24 [2 marks] Section 3.5 7) Page 234, Q. 4 [3 marks] 8) (a) Sketch the graph of f(x) = 7_TE (b) Find the domain and range R of f. (c) Find the interval on which f is increasing or is decreasing. [4 marks] 9) Identify any vertical asymptotes, horizontal asymptotes, and holes of f(x) = (3r+6) (x-2) (x-2](r+1) . [5 marks] 10) All asymptotes, intercepts, and holes of a rational function f are labeled in the figure below. Sketch a graph of f and find an equation for f. [4 marks] (6. 3.5) O 2 (-4,2) 11) Page 234, Q. 18 [4 marks] 12) Page 234, Q. 22 [4 marks] 13) Page 235, Q. 50 [4 marks]MATH 1001: Pre-Calculus Mathematics Assignment 3: Polynomial and Rational Functions (54 marks, 6%) Complete the following questions from the textbook. Show all your work, as full credit will not be given for inadequately explained answers. This assignment is worth 6% of your final grade and will be marked out of 54. For detailed instructions on how to submit your assignments go to "How to Send Assignments for Grading" in your Course Guide. Section 3.1 1) Sketch the graph of f(x) = ax + b, for a) a = -2, b = 0 [2 marks] b) a= =, b= -2 [2 marks] 2) Match each graph with an equation: [4 marks] a) b) c) d) I. f(x) = (x+ 1)(x - 1)(x +2) II. f(x) = (x - 1)(x - 2)(x - 3) III. f(x) = x3(x+2) IV. f(x) = -x(x -1) 3) Page 191, Q. 26 [4 marks] Section 3.2 4) Find the quotient and remainder if f(x) = 4x* + 10x3 + 18x - 1 is divided by p(x) = x + 3. [3 marks]