SECTION 3.1 Properties of Linear Functions and Linear Models 145 ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 3.1 Assess Your Understanding 1. Graph y x3 1. = − (pp. 32–35) 2. Find the slope of the line joining the points 2, 5 ( ) and 1, 3 . ( ) − (pp. 32–35) 3. Find the average rate of change of f x x4 3, ( ) = − + from 2 to 4. (pp. 93–94) 4. Solve: x x 60 900 15 2850. − = − + (pp. A44–A46) 5. If f x x 7.5 15, ( ) = + find f 2 . ( ) − (pp. 65–67) 6. True or False The function f x x 2 3 15 ( ) = + is increasing on the interval , . ( ) −∞ ∞ (pp. 89–90) (c) Figure 5 shows the graphs of S S p( ) = and D D p( ) = with the equilibrium point labeled. Figure 5 Supply and demand functions p 200 Equilibrium point 400 Price ($) Quantity supplied, Quantity demanded S 5 S(p) D 5 D(p) S, D 3000 2000 1000 (60, 0) (0, 2850) (200, 2100) Now Work PROBLEM 41 7. For the graph of the linear function f x mx b, ( ) = + m is the and b is the . 8. If the slope m of the graph of a linear function is , the function is increasing over its domain. 9. True or False The slope of a nonvertical line is the average rate of change of the linear function. 10. True or False The average rate of change of f x x2 8 ( ) = + is 8. 11. Multiple Choice What is the only type of function that has a constant average rate of change? (a) linear function (b) quadratic function (c) step function (d) absolute value function 12. Multiple Choice A car has 12,500 miles on its odometer. Say the car is driven an average of 40 miles per day. Choose the model that expresses the number of miles N that will be on its odometer after x days. (a) N x x 40 12,500 ( ) = − + (b) N x x 40 12,500 ( ) = − (c) N x x 12,500 40 ( ) = + (d) N x x 40 12,500 ( ) = + Concepts and Vocabulary In Problems 13–20, a linear function is given. (a) Find the slope and y-intercept of each function. (b) Use the slope and y-intercept to graph each function. (c) What is the average rate of change of each function? (d) Determine whether each function is increasing, decreasing, or constant. 13. f x x2 3 ( ) = + 14. g x x5 4 ( ) = − 15. h x x3 4 ( ) = − + 16. p x x 6 ( ) = − + 17. f x x 1 4 3 ( ) = − 18. h x x 2 3 4 ( ) = − + 19. F x 4 ( ) = 20. G x 2 ( ) = − Skill Building In Problems 21–28, determine whether each function is linear or nonlinear. If it is linear, determine the slope. x y f x( ) = 2− 4 1− 1 0 2− 1 5− 2 8− 22. x y f x( ) = 2− 14 1− 12 0 1 1 2 2 4 23. x y f x( ) = 2− 8− 1− 3− 0 0 1 1 2 0 24. x y f x( ) = 2− 4− 1− 0 0 4 1 8 2 12 21. 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
RkJQdWJsaXNoZXIy NjM5ODQ=