182 CHAPTER 3 Linear and Quadratic Functions ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 3.5 Assess Your Understanding 1. Solve the inequality x3 2 7 − − < . (pp. A80–A81) 2. Write 2, 7 ( ] − using inequality notation. (pp. A77–A78) Skill Building In Problems 3–6, use the figure to solve each inequality. 3. y 24 3 23 3 (22, 0) (2, 0) x y 5 f(x) (a) f x 0 ( ) > (b) f x 0 ( ) ≤ 4. y 22 2 4 22 24 5 (4, 0) (21, 0) (1.5, 5) x y 5 g(x) (a) g x 0 ( ) < (b) g x 0 ( ) ≥ 5. y 4 24 8 (22, 8) (1, 2) (2, 8) x y 5 g(x) y 5 f(x) (a) g x f x ( ) ( ) ≥ (b) f x g x ( ) ( ) > 6. y 212 3 23 6 (23, 212) (3, 212) (1, 23) x y 5 g(x) y 5 f(x) (a) f x g x ( ) ( ) < (b) f x g x ( ) ( ) ≥ In Problems 7–22, solve each inequality. 7. x x3 10 0 2 − − < 8. x x3 10 0 2 + − > 9. x x4 0 2 − > 10. x x8 0 2 + > 11. x 9 0 2 − < 12. x 1 0 2 − < 13. x x 12 2 + > 14. x x7 12 2 + <− 15. x x 2 5 3 2 < + 16. x x 6 6 5 2 < + 17. x x 1 0 2 − + ≤ 18. x x2 4 0 2 + + > 19. x x 4 9 6 2 + < 20. x x 25 16 40 2 + < 21. x x 6 1 5 2 ( ) − > 22. x x 2 2 3 9 2 ( ) − >− Mixed Practice In Problems 23–30, use the given functions f and g. (a) Solve f x 0. ( ) = (b) Solve g x 0. ( ) = (c) Solve f x g x . ( ) ( ) = (d) Solve f x 0. ( ) > (e) Solve g x 0. ( ) ≤ (f) Solve f x g x . ( ) ( ) > (g) Solve f x 1. ( ) ≥ 23. f x x g x x 1 3 3 2 ( ) ( ) = − = + 24. f x x g x x 3 3 3 2 ( ) ( ) = − + = − + 25. f x x g x x 1 4 1 2 ( ) ( ) = − + = + 26. f x x g x x 4 2 2 ( ) ( ) = − + = − − 27. f x x g x x 4 4 2 2 ( ) ( ) = − = − + 28. f x x x g x x 2 1 1 2 2 ( ) ( ) = − + = − + 29. f x x x g x x x 2 2 2 2 ( ) ( ) = − − = + − 30. f x x x g x x x 1 6 2 2 ( ) ( ) = − − + = − + + Applications and Extensions 96 ft s 5 80t 2 16t 2 31. What is the domain of the function f x x 16? 2 ( ) = − 32. What is the domain of the function f x x x3 ?2 ( ) = − 33. Physics A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s t t t 80 16 .2 ( ) = − (a) At what time t will the ball strike the ground? (b) For what time t is the ball more than 96 feet above the ground? 34. Physics A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s t t t 96 16 .2 ( ) = − (a) At what time t will the ball strike the ground? (b) For what times t is the ball more than 128 feet above the ground? 35. Revenue Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue R (in dollars) is R p p p 4 4000 2 ( ) = − + (a) At what prices p is revenue zero? (b) For what range of prices will revenue exceed $800,000? 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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