146 CHAPTER 3 Linear and Quadratic Functions 25. x y f x( ) = 2− 26 − 1− 4− 0 2 1 2− 2 10 − 26. x y f x( ) = 2− 4− 1− 3.5 − 0 3− 1 2.5 − 2 2− 27. x y f x( ) = 2− 8 1− 8 0 8 1 8 2 8 28. x y f x( ) = 2− 0 1− 1 0 4 1 9 2 16 29. Suppose that f x x4 1 ( ) = − and g x x2 5. ( ) = − + (a) Solve f x 0. ( ) = (b) Solve f x 0. ( ) > (c) Solve f x g x . ( ) ( ) = (d) Solve f x g x . ( ) ( ) ≤ (e) Graph y f x( ) = and y g x( ) = and label the point that represents the solution to the equation f x g x . ( ) ( ) = 30. Suppose that f x x3 5 ( ) = + and g x x2 15. ( ) = − + (a) Solve f x 0. ( ) = (b) Solve f x 0. ( ) < (c) Solve f x g x . ( ) ( ) = (d) Solve f x g x . ( ) ( ) ≥ (e) Graph y f x( ) = and y g x( ) = and label the point that represents the solution to the equation f x g x . ( ) ( ) = 31. In parts (a)–(f), use the figure below. x y (88, 80) (40, 50) (240, 0) y 5 f(x) (a) Solve f x 50. ( ) = (b) Solve f x 80. ( ) = (c) Solve f x 0. ( ) = (d) Solve f x 50. ( ) > (e) Solve f x 80. ( ) ≤ (f) Solve f x 0 80. ( ) < < 32. In parts (a)–(f), use the figure below. (215, 60) (5, 20) (15, 0) x y y 5 g(x) (a) Solve g x 20. ( ) = (b) Solve g x 60. ( ) = (c) Solve g x 0. ( ) = (d) Solve g x 20. ( ) > (e) Solve g x 60. ( ) ≤ (f) Solve g x 0 60. ( ) < < 33. In parts (a) and (b), use the figure below. x y (24, 6) y 5 g(x) y 5 f(x) (a) Solve the equation: f x g x . ( ) ( ) = (b) Solve the inequality: f x g x . ( ) ( ) > 34. In parts (a) and (b), use the figure below. x y (2, 5) y 5 g(x) y 5 f(x) (a) Solve the equation: f x g x . ( ) ( ) = (b) Solve the inequality: f x g x . ( ) ( ) ≤ 35. In parts (a) and (b), use the figure below. x y (5, 12) (0, 12) (0,25) (26,25) y 5 f(x) y 5 h(x) y 5 g(x) (a) Solve the equation: f x g x . ( ) ( ) = (b) Solve the inequality: g x f x h x . ( ) ( ) ( ) ≤ < 36. In parts (a) and (b), use the figure below. x y (0, 7) (24, 7) (0, 28) (7,28) y 5 h(x) y 5 g(x) y 5 f(x) (a) Solve the equation: f x g x . ( ) ( ) = (b) Solve the inequality: g x f x h x . ( ) ( ) ( ) < ≤ 37. Getting Towed The cost C, in dollars, to tow a car is modeled by the function C x x 2.5 85, ( ) = + where x is the number of miles towed. (a) What is the cost of towing a car 40 miles? (b) If the cost of towing a car is $245, how many miles was it towed? (c) Suppose that you have only $150. What is the maximum number of miles that you can be towed? (d) What is the domain of C? Applications and Extensions
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