96 CHAPTER 2 Functions and Their Graphs 10. True or False Even functions have graphs that are symmetric with respect to the origin. 11. Multiple Choice An odd function is symmetric with respect to . (a) the x-axis (b) the y-axis (c) the origin (d) the line y x = 12. Multiple Choice A function that is continuous on the interval is guaranteed to have both an absolute maximum and an absolute minimum. (a) a b , ( ) (b) a b , ( ] (c) a b , [ ) (d) a b , [ ] Skill Building In Problems 13–24, use the graph on the right of the function f. 13. Is f increasing on the interval 8, 2 ? [ ] − − 14. Is f decreasing on the interval 8, 4 ? [ ] − − 15. Is f increasing on the interval 2, 6 ? [ ] − 16. Is f decreasing on the interval 2, 5 ? [ ] 17. List the interval(s) on which f is increasing. 18. List the interval(s) on which f is decreasing. 19. Is there a local maximum at 2? If yes, what is it? 20. Is there a local maximum at 5? If yes, what is it? 21. List the number(s) at which f has a local maximum. What are the local maximum values? 22. List the number(s) at which f has a local minimum. What are the local minimum values? 23. Find the absolute minimum of f on 10,7. [ ] − 24. Find the absolute maximum of f on 10,7. [ ] − In Problems 25–32, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which the function is increasing, decreasing, or constant (d) Whether the function is even, odd, or neither x y 5 10 10 26 25 210 (0, 0) (28, 24) (25, 0) (210, 0) (22, 6) (2, 10) (5, 0) (7, 3) 25. x y 4 4 24 (0, 3) (24, 2) (2, 0) (4, 2) (22, 0) 26. x y 3 3 23 (3, 3) (23, 3) (0, 2) (1, 0) (21, 0) 27. x y 3 3 23 (0, 1) 28. x y 3 3 23 (1, 0) 29. , 1 p–– 2 2 p–– 2 , 21 ( ) ( ) p–– 2 2 p–– 2 x y 2 22 2p p 30. x y 2 22 2p 2 p (2p, 21) (p, 21) 2 p 2 p (0, 1) 31. x y 3 3 –3 –3 (–3, 2) (–1, 2) (3, 1) (1, –1) (2, –1) ( ) , 0 1 – 3 ( ) 0, 1 – 2 32. x y 3 3 22 23 (23, 22) (22, 1) (22.3, 0) (2, 2) (0, 1) (3, 0) In Problems 33–36, the graph of a function f is given. Use the graph to find: (a) The numbers, if any, at which f has a local maximum. What are the local maximum values? (b) The numbers, if any, at which f has a local minimum. What are the local minimum values? 33. x y 4 4 24 (0, 3) (2, 0) (22, 0) 34. x y 3 3 23 (0, 2) (1, 0) (21, 0) 35. x y p 2p , 1 p–– 2 2 p–– 2 , 21 ( ) ( ) p–– 2 2 p–– 2 1 21 36. x y 2 22 2p p (2p, 21) (p, 21) 2 (0, 1) p 2 p2
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