MHF4U1-ASSIGNMENT CHAPTER 1A

MHF4U1-ASSIGNMENT CHAPTER 1A NAME:______________________ True/False Indicate whether the statement is true or false. ____ 1. Even functions are symmetric about the x -axis. ____ 2. Odd-degree polynomials have at least one x- intercept. ____ 3. Even-degree polynomial functions always begin and end on the same side of the x -axis. ____ 4. The graph of a quartic function cannot have exactly three x -intercepts. ____ 5. The function y = x 5 – 5 x 3 + 7 is symmetric about the origin. Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 6. An equation representing a function that extends from quadrant 3 to quadrant 1 is a. y = x 3 c. y = 2 x 6 b. y = – 2 x 5 d. y = – 5 x 4 ____ 7. An equation representing a function that extends from quadrant 3 to quadrant 4 is a. y = x 3 + 7 x – 1 c. y = 2 x 6 – 4 x 3 b. y = – 2 x 5 + x – 1 d. y = – 5 x 4 – 2 x 2 – 1 ____ 8. The degree of the polynomial function y = x 3 – 2 x 2 + 5 x – 1 is a. 3 c. 5 b. 4 d. 6 ____ 9. The graph of the polynomial function y = – 2 x ( x – 1) 2 ( x – 2) 2 extends from a. quadrant 3 to quadrant 1 c. quadrant 2 to quadrant 1 b. quadrant 3 to quadrant 4 d. quadrant 2 to quadrant 4 ____ 10. The function y = 6( x – 1) 4 ( x – 2) 2 ( x + 1) changes sign at a. x = 1 c. x = – 1 b. x = 2 d. it doesn’t change sign ____ 11. Which of the following is a polynomial function? a. y = sin x c. y = 3 x b. y = cos x d. y = x 3 ____ 12. Which of the following is an even function? a. y = 2 x 4 + x 3 c. y = 2 x 4 – x b. y = 2 x 4 + 11 d. y = – x 3 + x 5 ____ 13. Which of the following graphs represents an even function?

a. c. b. d. ____ 14. Which of the following graphs represents an odd function? a. c. b. d. ____ 15. The number of times that the function y = ( x – 1) 3 ( x + 2)( x – 4) 2 changes sign is a. 0 c. 2 b. 1 d. 3 ____ 16. The function y = ( x – 4) 2 ( x – 7)( x + 3) 3 is negative on the intervals a. x  ( –  –  ) and x  (4, 7) c. x  ( –  4) and x  (7,  ) b. x  ( –   ) and x  (7,  ) d. x  ( –  4) and x  (4, 7) ____ 17. The table of values represents a polynomial function. x y – 3 6 – 2 2 – 1 0 0 0 1 2 2 6 The function is a. linear c. cubic

a. c. b. d. ____ 22. Which of the following graphs represents the function y = 2 x 5 – 3 x 4 + 1? a. c. b. d. ____ 23. Given the function y = ( x – 1) 2 ( x + 1) 2 , which finite differences will be equal (or constant)? a. first differences c. third differences b. second differences d. fourth differences ____ 24. Given the function y = – 3 x 2 – 5 x + 1, the second differences will all equal a. 3 c. 6 b. – 3 d. – 6 ____ 25. An equation for a cubic function with zeros 1, – 2, and 3 that passes through the point (2, 12) is a. y = x ( x + 2)( x – 3) c. y = – 3( x – 1)( x + 2)( x – 3) b. y = ( x – 1)( x + 2)( x – 3) d. ____ 26. An equation for a quintic function with zeros 1, 0, and 2 that passes through the point ( – 1, 24) is a. y = 2 x ( x – 1)( x + 2) 3 c. y = – 3( x – 1) 2 ( x – 2) 2 x 2 b. y = – 2 x 2 ( x – 1) 2 ( x – 2) d.

____ 27. State the interval(s) for which the graph of the function is negative. a. x  ( –  , -1) and x  (2,  ) c. x  ( –  , 0) and x  (2,  ) b. x  ( –  , 2) d. x  ( –  , 0) and x  (0,  ) Matching Match each item with its description below. a. quartic f. extends from quadrant 2 to quadrant 1 b. cubic g. extends from quadrant 2 to quadrant 4 c. quintic h. instantaneous rate of change d. never changes sign i. average rate of change e. even function j. is symmetric about the origin ____ 28. slope of the tangent ____ 29. y = – 2 x(x – 1)( x + 3) 2 ____ 30. y = 7 x 6 – 3 x 2 + 5 x ____ 31. y = x ( x 2 – 1) ____ 32. has between 1 and 5 x -intercepts ____ 33. y = – ( x – 1) 2 ( x + 4) 4 ____ 34. an odd function ____ 35. y = – 2 x 2 ( x – 1)( x + 3) 2 ____ 36. slope of the secant ____ 37. any function for which f ( x ) = f ( – x ) Completion Complete each statement. 38. The polynomial function y = x ( x – 1)( x + 2) 2 has _______________ x -intercepts. 39. The polynomial function y = 2 x 9 ( x 2 – 1) is an example of an _______________ (even/odd) function. 40. The graph of the function y = x 4 ( x – 1) 6 ( x + 2) 2 changes sign _______________ times. 41. For the polynomial function y = x 5 – 3 x 4 – x + 1, the _______________ differences will be constant (equal).

47.Determine an equation for the graph of the polynomial function shown. Problem 48. Determine an equation for the polynomial function represented in the table of values. x y – 3 0 – 2 – 4 – 1 – 6 0 – 6 1 – 4 2 0 3 6 49. Determine an equation for the quartic polynomial function represented by the table of values. x y – 3 91 – 2 21 – 1 3 0 1 1 3 2 21 3 91 50. Determine an equation in factored form for a polynomial function with zeros – 1 (order 2) and 3 (order 3) that passes through the point (4, 5)