Terms and Concepts 1. Why is sketching curves by hand beneficial even though technology is readily available? 2. T/F: When sketching graphs of functions, it is useful to find the critical points. 13. f(x) = x - 2x? + 4x + 1 14. f(x) = -x + 5x? - 3x+2 15. f(x) = x + 3x + 3x + 1 16. f(x) = x - x² – x+ 1 17. f(x) = (x - 2) In(x – 2) 3. T/F: When sketching graphs of functions, it is useful to find the possible points of inflection. 18. f(x) = (x- 2)² In(x- 2) x - 4 19. f(x) = 4. T/F: When sketching graphs of functions, it is useful to find the horizontal and vertical asymptotes. x² x - 4x + 3 20. f(x) = x2 – 6x + 8 Problems 21. f(x) = x+ sin x on (0, 27). x - 2x + 1 5. Given the graph of f, identify the concavity of f, its inflec- tion points, its regions of increasing and decreasing, and its relative extrema. 22. f(x) x2 %3D 6x + 8 23. f(x) = x/x+1 24. f(x) = x'e* 25. f(x) = sin x cos x on [-7, 7] 26. f(x) = (x - 3)2/3 + 2 (x – 1)2/3 27. f(x) = 28. f(x) = 29. f(x) = secx- 2 cos x on [0, 27]. 30. f(x) = x/2 – x2 31. f(x) = 6. Given the graph of f', identify the concavity of f, its inflec- tion points, its regions of increasing and decreasing, and its relative extrema. Vx? – 1 32. f(x) = x/3 - 5x/3 sin x 33. f(x) = on (0, 27). 2+ CoS X 34. f(x) = x2 + 3 2 4x – 4x + 1 35. f(x) = 4x2 - 12x + 9 Hint: f(x) can be simplified in a variety of ways whichever simplification works best for your curren 36. y = Vx2 + x - x 37. y = x + cos X 38. y = x tan x on (-,) In Exercises 7-12, practice using Key Idea 6 by applying the principles to the given functions with familiar graphs. 39. y = sin x+ V3 cos x on [-27, 27] 40. y = csc x - 2 sin x on (0, 7) 7. f(x) = 2x +4 3 41. f(x) = 8. f(x) = -x +1 x2 + 4 9. f(x) = sin x 42. f(x) = x2 4 10. f(x) = e 43. f(x) 1 11. f(x) = x2 + 4 44. f(x) = 1 12. f(x) = x2 4 x2 45. f(x) = X - 4 In Exercises 13-46, sketch a graph of the given function using Key Idea 6. Show all work; check your answer with technology. (x – 1) x2 + 1 46. f(x) =