SECTION 3.2 Building Linear Models from Data 149 Retain Your Knowledge Problems 59–68 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 59. Graph x x y y 4 10 7 0. 2 2 − + + − = 60. If f x x B x f 2 3 and 5 8, ( ) ( ) = + − = what is the value of B? 61. Find the average rate of change of f x x x 3 5 2 ( ) = − from 1 to 3. 62. Graph g x x x x x if 0 1 if 0 2 ( ) = ≤ + > ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ In Problems 63–64, complete the square for each quadratic function. 63. f x x x 10 7 2 ( ) = − + 64. g x x x 3 15 13 2 ( ) = + + 65. Find the x -intercept(s) and y -intercepts(s) of the graph of x y 4 9 72. 2 + = 66. Find the domain of f x x x 2 4 . ( ) = + − 67. Suppose f x x x3 7. 2 ( ) = − + Find an equation of the secant line containing the points f 1, 1 ( ) ( ) − − and f 2, 2. ( ) ( ) 68. Use a graphing utility to graph f x x x x 8 13 2 3 2 ( ) = − + − over the interval 2, 8 . [ ] − Then, approximate any local maximum values and local minimum values, and determine where f is increasing and where f is decreasing. Round answers to two decimal places. ‘Are You Prepared?’ Answers 1. 2221 x y 1 2 21 2 2. 2 3 3. 4− 4. 50 { } 5. 0 6. True 1 Draw and Interpret Scatter Plots In Section 3.1, we built linear models from verbal descriptions. Linear models can also be constructed by fitting a linear function to data that can be represented as ordered pairs. The first step is to plot the ordered pairs using rectangular coordinates. The resulting graph is a scatter plot . 3.2 Building Linear Models from Data Now Work the ‘Are You Prepared?’ problems on page 153. • Rectangular Coordinates (Section 1.1, p. 2) • Functions (Section 2.1, pp. 61–73) • Lines (Section 1.5, pp. 32–43) PREPARING FOR THIS SECTION Before getting started, review the following: OBJECTIVES 1 Draw and Interpret Scatter Plots (p. 149) 2 Distinguish between Linear and Nonlinear Relations (p. 150) 3 Use a Graphing Utility to Find the Line of Best Fit (p. 152) Drawing and Interpreting a Scatter Plot In baseball, the on-base percentage for a team represents the percentage of time that the players safely reach base. The data given in Table 6 on the next page represent the number of runs scored y and the on-base percentage x for teams in the National League during a recent baseball season. (a) Draw a scatter plot of the data, treating on-base percentage as the independent variable. (b) Use a graphing utility to draw a scatter plot. (c) Describe what happens to runs scored as the on-base percentage increases. EXAMPLE 1 (continued)
RkJQdWJsaXNoZXIy NjM5ODQ=