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]3.1 Polynomial Functions of Degree Greater Than 2 191 (c) (d) 29 /(x) = (x + 2)(x - 1)3(x - 2) 30 /(x) = x(x + 1)'(x - 2)(x - 4) Exer. 31-32: Sketch the graph of a polynomial given the 7 1 sign diagram. 31 Sign of f(x) (A) f(x) = x(x - 1) (B) f(x) = -xx + 2) 3.2 (C) f(x) = (x + 2)(x+ 1)(x - 3) Sign of f(x) + (D) (x) = (x + 2)(x + 1(x - 1) -3 -2 0 Exer. 13-14: Use arrow notation to describe the end behav- 33 (a) Sketch a graph of ior of the function. Do not sketch the graph. f(x) = (x - a)(x - b)(x - c). 13 (a) /(x) = 3x - 2r + 6 where a (? (d) fux) = -2+ 3x -6 (d) What is the solution to /(x) = (? 35 Let f(x) be a polynomial such that the coefficient of every Exer. 15-30: Find all values of r such that f(x) > 0 and all r odd power of x is 0. Show that f is an even function. such that f(r) 0 and all x such that P(x)