186 CHAPTER 3 Linear and Quadratic Functions The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. 1. For the linear function f x x4 3: ( ) = − + (a) Find the slope and y-intercept. (b) What is the average rate of change of f ? (c) Determine whether f is increasing, decreasing, or constant. (d) Graph f. In Problems 2 and 3, find the intercepts, if any, of each quadratic function. 2. f x x x 3 2 8 2 ( ) = − − 3. G x x x 2 4 1 2 ( ) = − + + 4. Suppose f x x x3 2 ( ) = + and g x x5 3. ( ) = + (a) Solve f x g x . ( ) ( ) = (b) Graph each function and label the points of intersection. (c) Solve the inequality f x g x ( ) ( ) < and graph the solution set. 5. Graph f x x 3 2 2 ( ) ( ) = − − using transformations. 6. Consider the quadratic function f x x x 3 12 4. 2 ( ) = − + (a) Is the graph concave up or concave down? (b) Find the vertex. (c) Find the axis of symmetry. (d) Find the intercepts. (e) Use the information from parts (a)–(d) to graph f. 7. Determine whether f x x x 2 12 3 2 ( ) = − + + has a maximum or a minimum. Then find the maximum or minimum value. 8. Solve x x 10 24 0. 2 − + ≥ 9. RV Rental The weekly rental cost of a 20-foot recreational vehicle is $129.50 plus $0.15 per mile. (a) Find a linear function that expresses the cost C as a function of miles driven m. (b) What is the rental cost if 860 miles are driven? (c) How many miles were driven if the rental cost is $213.80? 10. Maximizing Revenue The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x p 10 10,000 = − + (a) Find a model that expresses the revenue R as a function of p. (b) What is the domain of R? Assume R is nonnegative. (c) What price p maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) What price should the company charge to earn at least $1,600,000 in revenue? Chapter Test (b) Based on the scatter plot, do you think that there is a linear relation between the length of the right humerus and the length of the right tibia? (c) Use a graphing utility to find the line of best fit relating length of the right humerus and length of the right tibia. (d) Predict the length of the right tibia on a rat whose right humerus is 26.5 millimeters (mm). Source: NASA Life Sciences Data Archive. Right Humerus (mm), x Right Tibia (mm), y 24.80 24.59 24.59 24.29 23.81 24.87 25.90 26.11 26.63 26.31 26.84 36.05 35.57 35.57 34.58 34.20 34.73 37.38 37.96 37.46 37.75 38.50 30. Advertising A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars). Total Revenue ($1000s) Advertising Expenditures ($1000s) 20 22 25 25 27 28 29 31 6101 6222 6350 6378 6453 6423 6360 6231 (a) Draw a scatter plot of the data. Comment on the type of relation that may exist between the two variables. (b) The quadratic function of best fit to these data is R A A A 7.76 411.88 942.72 2 ( ) = − + + Use this function to determine the optimal level of advertising. (c) Use the function to predict the total revenue when the optimal level of advertising is spent. (d) Use a graphing utility to verify that the function given in part (b) is the quadratic function of best fit. (e) Use a graphing utility to draw a scatter plot of the data, and then graph the quadratic function of best fit on the scatter plot.
RkJQdWJsaXNoZXIy NjM5ODQ=