Math 1325 Review #1



Math 2412 Review 2

Sketch the graphs of the following polynomial functions.(1-4) Label the zeros and y-intercept.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

Sketch the graphs of the following rational functions.(5-8) Label asymptotes and intercepts.

5. [pic] 6. [pic]

7. [pic] 8. [pic]

Solve the following inequalities by completing the sign charts, and expressing the solution in

interval notation.(9-12)

9. [pic] 10. [pic]

11. [pic] 12. [pic]

13. Approximate a solution of the polynomial equation [pic] using the Bisection Method by completing the following table:

|Left Endpoint(sign) |Midpoint(sign) |Right Endpoint(sign) |Error Bound |

|1(-) |[pic](-) |2(+) |[pic] |

|[pic](-) |[pic](-) |[pic](+) |[pic] |

| | | | |

| | | | |

Find partial fraction decompositions for the following.(14-16)

14. [pic] 15. [pic] 16. [pic]

17. The first step in finding the partial fraction decomposition of [pic] would be to divide the numerator by the denominator. Perform this division.

Sketch the graphs of the following exponential and logarithmic functions. Indicate the asymptotes and intercepts.(18-21)

18. [pic] 19. [pic]

20. [pic] 21. [pic]

Find the exact simplified value of the following expressions.(22-29)

22. [pic] 23. [pic] 24. [pic]

25. [pic] 26. [pic] 27. [pic] 28. [pic]

29. [pic]

Expand the following logarithmic expressions as much as possible. Simplify if possible.

30. [pic] 31. [pic]

Compress the following logarithmic expressions into a single term. Simplify if possible.

32. [pic] 33. [pic]

34. Evaluate [pic] using a calculator to four decimal places.

35. Solve the inequality [pic]. You may use the given graphs of [pic] and [pic], if you like.

Solve the following equations.(36-48)

36. [pic] 37. [pic] 38. [pic] 39. [pic]

40. [pic] 41. [pic] 42. [pic] 43. [pic]

44. [pic] 45. [pic]

46. [pic] 47. [pic] 48. [pic]

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[pic]

[pic]

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