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Accelerated Integrated Algebra I Name _________________________ Final Exam Review – Fall 2010 Answer each problem completely on a separate sheet (or sheets) of paper in an organized way. 1. Determine the equation of the line through the 2 25. Graph y 3 . State the domain and points (4, 7) and (2, 10). x 1 2. Compare the rate of change of a linear function, range. quadratic function and cubic function. 26. Determine the asymptotes of the graph of 3. Graph y x 5 . 1 y 7. 2x 6 4. State the domain and range of y x 8 3 . x 2 26x 48 3x 12 5. State the domain and range of y x 2 6x 5 . 27. Simplify: . x 2 6x 8 x 2 4 6. State the domain and range of y = 3x + 2. x 3 5x 2 6x 8x 3 7. Factor completely: 100x 2 25y 2 . 28. Simplify: . 2x 4 x 3 8. Factor completely: 2x 2 26x 72 . 3 x 1 29. Add: . 9. Factor completely: x 3 3x 2y 3xy 2 y 3 . x 2 x 2 10. Find the zeros: f (x ) x 2 2x 15 . 6 x 30. Subtract: . 11. Find the zeros: f (x ) 2x 2 11x 21 . x 2 5x 50 x 2 9x 20 12. Use the Quadratic Formula to solve 31. Convert to vertex form: y x 2 10x 3 . 3x 2 9x 7 0 . 32. Find the axis of symmetry: y x 2 11x 18 . 13. Express as a complex number in standard form: 33. Find the x- and y-intercepts: y 3x 2 x 10 . 81 2 . 34. Determine the solution to f(x) = g(x). 14. Express as a complex number in standard form: (2 7i )(5 4i ) . 15. Express as a complex number in standard form: 1 3i . 8 7i 16. Express as a complex number in standard form: (5 100) (3 6i ) . 1 17. Graph g (x ) x 4 2 . Explain the 3 transformations represented by this function. 18. Graph y x 2 9 . Discuss the end behavior of the graph. 35. Solve f(x) = g(x) if f(x) = 3x - 2 and g(x) = x2. 2 19. Sketch the graph of a function with the 36. Solve: x 9 10 14 . following end behavior: 37. Solve: x 2 9x 22 . As x ,f (x ) . As x ,f (x ) . 1 38. Solve: 3x 1 2 . 20. Determine whether the function is odd, even or 4 neither: y x 3 1 . 3 5 2 39. Simplify: . 21. Determine whether the function is odd, even or 3 neither: 40. Simplify: . 8 4 41. Simplify: . 1 7 42. The maximum walking speed S (in feet per second) of an animal is given by the function S 32L where L is the length of the animal’s legs (in feet). How fast can an animal whose legs are 18 inches long walk? 22. Explain two ways to tell that a function is odd. 43. Write a rule for a radical function with domain 23. Divide: 4x 2 8x 9 2x 1 . x 3 and range y 1 . x 7 24. Divide: 16x 2 49 4x 7 . 44. Simplify: x 16x 63 2 . 45. Determine the asymptotes of the graph of 63. Find the equation of the line parallel to 2x 9 y = 2x – 9 that passes through the point (1, 4). y x 5 64. Joe’s cell phone plan costs $45 per month and includes 750 free anytime minutes. There is a 46. Represent the area of the rectangle as a $0.49 per minute charge for every additional polynomial expression. minute. Write an equation to represent Joe’s monthly cell phone charges. 2x - 1 65. Find f(4) for f(x) = 2x2 + 4x – 3. 66. f(x) = 9x – 11. Find x when f(x) = 12. 3x + 7 67. A roof shingle is dropped from 100 ft above the 47. Find the formula that generates the sequence: ground. The height y (in ft) of the dropped 3, 9, 15, 21, 27, . . . shingle is given by the function y = -16t2 + 48. Find the formula that generates the sequence: 100 where t is the time (in sec) since the shingle 3, 12, 48, 192, 768, . . . is dropped. Estimate when the shingle is at a 49. What type of sequence is 12, 9, 6, 3, 0, -3, . . .? height of 50 feet. Explain. 68. Compare the graph of g(x) = x2 + 4 to 50. Write a polynomial expression that repesents f(x) = x2 – 3. only the shaded area: 1 69. Find the vertex of y x 2 4x 5 . 3 10 70. Describe the graph of y 4(x 2)2 10 . x 71. Find the zeros of the function by graphing: f (x ) 3x 2 6x 24 . 72. Graph y x 3 2 . 19 73. Explain how to find the asymptotes of a rational x + 23 function. 4 74. Explain how to find the excluded values of a 51. Expand: 2x 3 . rational expression. 5 52. Expand: x 2 . 75. Determine the function graphed below. 2 53. Find the product: 3x 8 . 54. Find the product: (2x + 5)(x2 – 3). 55. Find the product: (4x + 11)(2x + 7). 56. Write a polynomial expression that represents the perimeter of the polygon: x + 21 5x - 8 4x + 13 x +1 2 76. Determine the function graphed below. 57. Identify the degree and leading coefficient of 5x 7 4x 3 2x 3x 10 . 58. Find the difference: (9x 11) (7x 2 8) . 59. Find the product: (2x 3 7x 2 x 3)(5x 2 4) . 60. Identify the slope of the line with the equation 2x + 5y = 15. 61. Identify the y-intercept of the line with the equation 3x – 7y = 11. 62. Determine the equation of the line.