MHF4U1 ASSIGNMENT CHAPTER 1 NAME: K /11 T/I: /11 A: /10 C: /10 Multiple Choice [K: 1 mark each = 33 total marks] Identify the choice that best completes the statement or answers the question. 1. An equation representing a function that extends from quadrant 3 to quadrant 1 is [1T] a. y=x3 C. y = 2x6 b. y=-2x d. y=-5x+ 2. An equation representing a function that extends from quadrant 3 to quadrant 4 is [1T] a. y=x +7x-1 C. y = 2x6 - 4x3 b. y=-2x +x-1 d. y=-5x4 -2x2 - 1 3. The function y = 6(x - 1)*(x -2)(x + 1) changes sign at [1T] a. x=1 C. x =-1 b. x =2 d. it doesn't change sign 4. Which of the following is a polynomial function? [1K] a. y = sin x C. y = 3x b. y = cos x d. y=x3 5. Which of the following graphs represents an even function? [1K] a. C. b. d . 6. The number of times that the function y = (x - 1) (x + 2)(x -4) changes sign is [1T] a. 0 C. 2 1 d.MHF4U1 ASSIGNMENT CHAPTER 1 NAME: 7. Which of the following graphs represents an odd function? [1K] a. C . b . d. 8. The function y = (x - 4)'(x - 7)(x + 3)' is negative on the intervals [1A] a. x E (-0, -3) and x E (4, 7) C. x E (-3, 4) and x E (7, 0.) . x E (-0, 3) and x E (7, 0.) d. x E (-3, 4) and x E (4, 7) 9. The table of values represents a polynomial function. [1K] - 3 6 -2 ON -1 0 0 N 2 6 The function is a. linear C. cubic P b. quadratic quarticMHF4UI ASSIGNMENT CHAPTER 1 NAME: 10. The least possible degree of the polynomial function represented by the graph shown is [1 T] U142- 11. An equation for the graph shown is [1A] MHF4UI ASSIGNMENT CHAPTER 1 NAME: 12. The graph of the function y = x(x 1)3(x + 2)2 would most closely resemble [IT] a. ' c. ' l) r b ' d 13. Which of the following graphs represents the Jnction y = 2x5 3x"1 + 1? [IT] a. ' { c. ' o 1- b " d 14. Given the function y = (x 1)3(x + 1)3, which nite differences will be equal (or constant)? [1K] a. rst differences c. third differences b. second differences (1. fourth differences 15. An equation for a cubic inction with zeros 1, 2, and 3 that passes through the point (2, 12) is [1A] a. y = x(x + 2)(x 3) c. y = 3(x 1)(x + 2)(x 3) b. y:(x*1)(x+2)(x'3) y=%(x+1)(x'2)(x+3) 16. An equation for a quintic function with zeros 1, 0, and 2 that passes through the point (71, 24) is [1A] a. y = 2x(x 1)(x + 2)3 c. = 3(x 1)2(x 2)3.r2 b. y:72r(xi 1mm y=x3(x_1;.(x2> 17. Given a function of the form y : a[k(x i (1)]\" + c, where k > 0, the transformation that occurs by changing the value off: is [1K] a. a horizontal stretch or compression c. a vertical translation b. a vertical stretch or compression (1. a reection in the xaxis MHF4UI ASSIGNMENT CHAPTER 1 NAME: 18. A secant drawn through the points shown on the graph has a slope of [1K] c. 3 d. 6 19. The average rate of change of the functiony = x3 x 1 om x = 1 to x = 4 is [1K] a. 1 c. 2.2 b. 2 d. 11 20. The number of people, P, at a playground alter t min is given by P = t3 + 4: + 20. The average rate of change of the number of people at the playground from 3 min to 4 min is [1K] a. 39 people/min c. 59 people/min b. 41 people/min d. 100 people/min 21. The number of people, P, at a playground after (min is given by P : (3 + 4: + 20.. The instantaneous rate of change of the number of people at the playground alter 1 min is approximately [1K] a. 5 people/min c. 7 people/min b. 6 people/min d. 25 people/min 22. The slope of the tangent at the point indicated on the graph is [1K] a 1 c. 2 2 MHF4UI ASSIGNMENT CHAPTER 1 NAME: Short Answers 1. Determine an equation for the graph of the polynomial function shown. [4T] 2. The number oftoy kangaroos, K, in a toy box after t days is given by K = :1 + 20:. Estimate the instantaneous rate at which the number of kangaroos is changing after 3 days. [3A] 3. The amount of money, M, in dollars, in a piggy bank after 1* days is given by M = 2:3 + 2! + II]. Estimate the instantaneous rate of change of the amount of money in the piggy bank aer 2 days. [3A] MHF-'lUI ASSIGNMENT CHAPTER I NAME: 4. Explain why odd-degree polynomial functions can have only local maximums and minimums, but not have absolute maximums and minimums. [C2] 5. Explain why even-degree polynomial functions can have both the local and absolute maximums and minimums. [C2] 6. Explain the reason why 81 = x4 would have 2 answers. [C2] 7. Haleh graphed the cubic function f(x) = x3 8x2, and then vertically translated the graph 1 down. Does the resulting graph have fewer zeros, the same number of zeros, or more zeros than the original graph? [C2] 8. If the value of k is unknown, which of the following characteristics of the graph of Ex) : k(x + 14)(x 13)(x + 15)(x -16) cannot be determined: the x-intercepts, the shape of the graph near each zero, the end behaviours, or the maximum number of turning points? Explain [C2]