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Name ______________________ Period_________ Semester Exam Review 1. How many real zeros does f x x 6x3 3x2 14x 2 have?_____________________ 4 2. Find the roots of f ( x) x3 5 x 2 3x 11 _________________________ 3. Find the values of x, if any, for which the following functions have a relative maximum or a relative minimum. a) f ( x) 4 x3 5 x 2 28 x 13 _________________ c) b) f ( x) x3 5x 2 4 x 13 _____________________ f ( x) 2 x2 3x 4 ___________________ 4. Describe the transformations compared to the parent graph. a) y x 2 7 ________________________________________________ b) y x 5 8 ___________________________________________________ c) y 3x 18 2 ______________________________________________ d) y 4 x 12 6 ______________________________________________ e) y x 2 8 x 11 ________________________________________________ 2 3 5. State the equation of the function generated by translating the parent graph _____________________________________________ 6. Find the inverses of the following functions a) f ( x) ( x 9)3 __________________ b) f ( x) x 2 5 ____________________ y x3 four units to the right and 8 units up. 7. What is the minimum possible degree of the polynomial of each function graphed? What is the function that describes the graph? a) b) c) d) 8. For x 2 5, x 3 , what is the value of f (3) ? f ( x) x 7, x 3 ______________ 9. Find the slope and y-intercept of the equation of the line passing through (-10,8) and (7, 3). 10. Write the slope intercept form of the equation of the line parallel to y = 3 x – 6 & passing through (0, 4). 4 11. Write the slope intercept form of the equation of the line perpendicular to y = -3x – 6 and passing through the point (7, -8). 12. Given f(x) = a) (f + g)(x) 2 and g(x) = x2- 3, find each function. x4 b) (f – g)(x) c) f g 13. Given: f(x) = 1 x+5 3 g(x) = x – 3 a) Find [f g](x) b) Find [g f ](x) ________________________ ________________________ Find the inverse of the function. Is the inverse a function? Write yes or no. 14. y = 6 – 2x 15. Given f(x) = 8- x2, find f (-2). _______________________ Find the critical points of each function. Then determine whether each point represents a maximum, minimum, or a point of inflection. 16. y = x 3 3x 2 4 17. ______________________ y 4 x x2 _____________________ 18. Find the x- and y-intercepts of y x 2 6 x 11.__________________________ 19. Describe the transformation(s) that have taken place from the parent graph of 2 f(x) = x . a) y=5x 2 ____________________________________________ 2 b) y = -.75 x ___________________________________________ c) y = 3(x – 5) __________________________________________ d) y = 2 1 2 (x + 4) 3 - 2 ______________________________________ 20. Which graph has a maximum point? a) y= x 2 +6x + 11 ______________ b) y = x 2 + 8x + 21 c) y = -5x 2 - 30x + 51 ______________ _______________ d) y = 8x 2 + 40x + 37 ________________ 21. What is the relative maximum point of the graph of y = -x 2 - x +3?_________________ 24. What point is a relative minimum of the graph of f(x) = x3 - 4x 2 -5x +14?_______________ 25. Write the polynomial equation of least degree for the set of roots 4i, -5 ________________ 26. Write the polynomial equation of least degree for the set of roots 6, -5, 3_______________ 27. Solve the equation by using the quadratic formula 3x2 - 12x + 4 = 0.____________________ 28. Find the remainder for each division using synthetic division. Is the binomial a factor of the polynomial? x4 x2 2 x3 Simplify. 29. (j5)-2 (j4)-5 9 30. 36 y 3y2 Evaluate using upside-down division. 31. 4 243x7 y 3 32. 75s8 33. Simplify i33. 34. Simplify (5 – 3i) + (-10 – 8i) 35. Simplify (3 - i)(4 + 2i) 36. Simplify 1 + 3i 2 + 5i 37. Complete the following Trig Identities. a) sin =______________ d) csc = _____________ b) cos =_______________ e) sec = ______________ c) tan = ______________ f) cot = _______________ 38. For right triangle ABC, if A = 22o, B = 90o, c = 10, find the measure of side b. 39. For right triangle ABC, if A = 22o, B = 90o, c = 10, find the measure of side a. 40. In ABC, a = 5, b = 6, and c = 8. Find the measure of angle B. 41. In ABC, a = 5, b = 6, and c = 8. Find the measure of angle C. 42. In ABC, A = 63o, B = 19o, and a = 2.4. Find b to the nearest tenth. 43. In ABC, a = 5, b = 6, and c = 8. Find the measure of angle A. 44. In ABC, A = 112.0o, B = 21.8o, and c = 18. Find a to the nearest tenth. 45. Sean, who is 56 meters from the base of a tower, measures 17 o to the top of the tower. How high is the tower? 46. A train travels due west for 400 kilometers and then north for 350 kilometers. Find the train’s distance and direction from its starting point. II. Find the values of the six trigonometric functions of . Assume that is an angle in standard position whose terminal side lies in the given quadrant. Draw and label the right triangle on the x-y plane. 47. sin 13 17 Quadrant II III. Find the values for State 49. 1 2 __________ 5 7 Quadrant III for which each equation is true. Draw the angles. in radians between sin 48. tan 0 and 2 . 50. sin 1 2 __________ 51. cos 52. 3 2 54. __________ 55. cos cos __________ 53. sin 1 2 1 2 __________ sin 0 __________ 3 2 __________ III. Sketch the angle on the unit circle. Find and label the reference angle. Find each exact value. Do NOT use a calculator. 56. 57. cos 58. 59. 5 3 sin 13 4 5 tan 6 sin 60. cos 2 3 9 4 3 2 61. tan 62. sin 3 Graph the following angles and label using both degree and radian measures. You will need a protractor for these problems. You can use back of this paper or another sheet to draw the angles. Radians measures will have a Pi symbol in it. 63. 84 66. 64. -350 16 9 67. 114 65. 10 13 68. 14 11 If each angle has the given measure and is in standard position, determine the quadrant in terminal side lies. 69. a) 7 12 b) 346 c) 25 13 D) 545 Find the reference angle for each angle with the given measure. 70. a) 300 b) 7 3 c) 645 d) 15 7 which its