Calculus/Precalculus/Exercises

Graphing linear functions Hyperbolic logarithm and angles Algebra Convert to interval notation 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. State the following intervals using set notation 11. 12. 13. 14. 15. 16. Which one of the following is a true statement? Hint: the true statement is often referred to as the triangle inequality. Give examples where the other two are false. 17. false 18. false 19. true Evaluate the following expressions 20. 21. 22. 23. 24. 25. 26. 27. 28. Simplify the following 29. 30. 31. 32. 33. 34. 35. 36. Find the roots of the following polynomials 37. 38. 39. 40. 41. 42. 43. 44. Factor the following expressions 45. 46. 47. Simplify the following 48. 49. 50. 51. Functions 52. Let . a. Compute , , and . , , and b. What are the domain and range of ? Domain is ; range is c. Does have an inverse? If so, find a formula for it. No, is not one-to-one. For example, both and result in . 53. Let , . a. Give formulae for i. ii. iii. iv. v. vi. vii. viii. b. Compute and . c. Do and have inverses? If so, find formulae for them. 54. Does this graph represent a function? Image:Sinx over x.svg Yes. 55. Consider the following function a. What is the domain? b. What is the range? c. Where is continuous? 56. Consider the following function a. What is the domain? b. What is the range? c. Where is continuous? 57. Consider the following function a. What is the domain? b. What is the range? c. Where is continuous? 58. Consider the following function a. What is the domain? b. What is the range? c. Where is continuous? Graphing 59. Find the equation of the line that passes through the point (1,-1) and has slope 3. 60. Find the equation of the line that passes through the origin and the point (2,3). Solutions Graphing linear functions Limits