216 Chapter 2 Linear Equations in Two Variables and Functions 53. Suppose that a student has an 80% average on all of her chapter tests in her Intermediate Algebra class.This counts as of the student’s overall grade.The final exam grade counts as the remaining of the student’s overall grade.The student’s overall course grade,G(x), can be computed by 3 4 1802 1 4 x, G(x) where x is the student’s grade on the final exam. a. Is this function linear, quadratic, or neither? b. Evaluate G(90) and interpret its meaning in the context of the problem. c. Evaluate G(50) and interpret its meaning in the context of the problem. 54. The median weekly earnings, E(x) in dollars, for women 16 yr and older working full time can be approximated by E(x) 0.14x2 7.8x 540. For this function, x represents the number of years since 2000. (Source: U.S. Department of Labor) a. Is this function linear, quadratic, or neither? b. Evaluate E(5) and interpret its meaning in the context of this problem. c. Evaluate E(10) and interpret its meaning in the context of this problem. For Exercises 55–60, write a function defined by y f(x) under the given conditions. 55. The value of f(x) is two more than the square of x. 56. The value of f(x) is the square of the sum of two and x. 57. The function f is a constant function passing through the point (4, 3). 58. The function f is a constant function with y-intercept (0, 5). 12 59. The function f is a linear function with slope and y-intercept (0, –2). 2 60. The function f is a linear function with slope 4 and y-intercept . 10, 13 14 3 4 Graphing Calculator Exercises For Exercises 61–66, use a graphing calculator to graph the basic functions.Verify your answers from the table on page 207. 61. f 1x2 x 62. f 1x2 x2 63. f 1x2 x3 64. 65. 66. For Exercises 67–70, find the x- and y-intercepts using a graphing calculator and the Value and Zero features. 4 5 1 8 67. 68. 69. 70. y 7 2 y x 4 y x 7 1 2 y x 1 x 3 f 1x2 1 x f 1x2 f 1x 1x2 x
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