6.10 Functions and Their Graphs 401 35. f x x x x ( ) 4 6 9, 3 2 = − − = − 45 36. f x x x x ( ) 3 2 5, 4 2 = + − = − 35 37. f x x ( ) 4 , 2 x = = − 1 16 38. f x x ( ) 3 , 4 x = = − 1 81 39. f x x ( ) , 2 x 1 3 ( ) = = − 9 40. f x x ( ) , 3 x 1 5 ( ) = = − 125 In Exercises 41– 46, graph the linear function by using the slope and y-intercept. 41. = − + f x x ( ) 3 * 42. = + f x x ( ) 2 1 * 43. f x x ( ) 3 2 = − + * 44. f x x ( ) 2 5 = + * 45. = − f x x ( ) 1 3 2 * 46. f x x ( ) 3 1 2 = − + * In Exercises 47–52, for the graph of each quadratic equation, a) determine whether the parabola opens upward or downward. b) determine the equation of the axis of symmetry. c) determine the coordinates of the vertex. 47. = − + y x x6 8 2 * 48. y x x8 12 2 = − + * 49. = − − − y x x 5 60 11 2 * 50. = − + − y x x 7 84 199 2 51. = − − + y x x 2 5 1 2 * 52. = − − y x x 4 11 3 2 * In Exercises 53– 60, for the graph of each quadratic function, a) determine whether the parabola will open upward or downward. b) determine the equation of the axis of symmetry. c) determine the vertex. d) determine the y-intercept. e) determine the x-intercepts if they exist. f) graph the function. g) determine the domain and range of the function. 53. = − f x x ( ) 1 2 * 54. = − f x x ( ) 9 2 * 55. = − + f x x ( ) 4 2 * 56. = − + f x x ( ) 16 2 * 57. = + − f x x x ( ) 2 8 2 * 58. = + + f x x x ( ) 8 12 2 * 59. f x x x ( ) 4 12 2 = − + + * 60. f x x x ( ) 6 8 2 = − + − * In Exercises 61–70, graph the exponential function and state the domain and range. 61. = y 3x * 62. f x( ) 4x = * 63. y x 1 3 ( ) = * 64. y x 1 4 ( ) = * 65. f x( ) 2 1 x = + * 66. = − y 3 1 x * 67. = + y 4 1 x * 68. = − y 2 1 x * 69. = − y 3x 1 * 70. f x( ) 4x 1 = + * Problem Solving In Exercises 71–86, when necessary, round your answers to the nearest hundredth. 71. Kettle Corn Weekly Profits Noah sells kettle corn at the farmers market. His profit, p x( ), in dollars can be estimated by the function = − p x x ( ) 2.5 45, where x is the number of bags of kettle corn sold. a) Determine the number of bags of kettle corn Noah must sell to break even, that is, to have profit equal to $0. 18 bags b) If Noah, sells 100 bags of kettle corn, estimate his profit. $205 c) If Noah has a profit of $300, how many bags of kettle corn did he sell? 138 bags 72. Salary Plus Commission Ashanti works as an appliance sales representative. Ashanti’s monthly salary, s x( ), is given by the function = + s x x ( ) 2600 0.15 , where x represents their monthly sales, in dollars. a) What is Ashanti’s monthly salary if their monthly sales are $7200? $3680 b) Determine the monthly sales needed for Ashanti to have a monthly salary of $5000 $16,000 73. Golfing on the Moon On February 6, 1971, astronaut Alan Shepard hit a golf ball while standing on the moon. The height of the ball, h t( ), above the moon’s surface, in feet, can be determined using the quadratic function, = − + h t t t ( ) 2.65 26.5 , 2 where t is the time, in seconds, after the ball is hit. a) What is the height of the ball after one second? 23.85 feet b) What is the height of the ball after five seconds? 66.25 feet c) What is the height of the ball after ten seconds? 0 feet $ $ *See Instructor Answer Appendix Wileydoc/Shutterstock
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