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3.7 Notes

3.7 Notes. Graphing Rational Functions. 3.7 Notes. Find and plot x and y intercepts. Use limit theorems to find and graph the discontinuities. a. Check for holes. b. Check for horizontal asymptotes. c. Check for slant asymptotes. d. Check for vertical asymptotes.

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3.7 Notes

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  1. 3.7 Notes Graphing Rational Functions

  2. 3.7 Notes • Find and plot x and y intercepts. • Use limit theorems to find and graph the discontinuities. a. Check for holes. b. Check for horizontal asymptotes. c. Check for slant asymptotes. d. Check for vertical asymptotes. • Use limits to determine the behavior of the graph between discontinuities. • Sketch a smooth curve.

  3. Example 1: Step 1. Find and plot x and y intercepts.

  4. Example 1:

  5. Example 1: Step 2. Find and graph discontinuities. a. no holes b/c no common factors in the num. and den. b. there is a horiz. asy. b/c deg. of num. = deg. of den.

  6. Example 1: Step 2. Find and graph discontinuities. c. no slant asy. b/c there is a horiz. asy. d. x = – 4 makes den. = 0

  7. Example 1:

  8. Example 1: Step 3. Use limits to determine behavior of graph around discontinuities.

  9. Example 1:

  10. Example 1: Step 4. Sketch a smooth curve.

  11. Example 2: Step 1. Find and plot x and y intercepts.

  12. Example 2: Step 1. Find and plot x and y intercepts.

  13. Example 2:

  14. Example 2: Step 2. Find and graph discontinuities.

  15. Example 2:

  16. Example 2: Step 3. Use limits to determine behavior of graph around discontinuities.

  17. Example 2:

  18. Example 2: Step 4. Sketch a smooth curve.

  19. Example 3: Step 1. Find and plot x and y intercepts.

  20. Example 3: Step 1. Find and plot x and y intercepts.

  21. Example 3:

  22. Example 3: Step 2. Find and graph discontinuities.

  23. Example 3:

  24. Example 3: Step 3. Use limits to determine behavior of graph around discontinuities.

  25. Example 3:

  26. Example 3: Step 4. Sketch a smooth curve.

  27. Practice Problems: 1. 2. 3.

  28. Practice 1: Step 1. Find and plot x and y intercepts.

  29. Practice 1: Step 2. Find and graph discontinuities. a. no holes b/c no common factors in the num. and den. b. is a horizontal asymptote. c. no slant asy. b/c there is a horiz. asy. d. are vertical asymptotes.

  30. Practice 1: Step 3. Use limits to determine behavior of graph around discontinuities.

  31. Practice 1: Step 3. Use limits to determine behavior of graph around discontinuities.

  32. Practice 1: Step 4. Sketch a smooth curve.

  33. Practice 2: Step 1. Find and plot x and y intercepts.

  34. Practice 2: Step 1. Find and plot x and y intercepts.

  35. Practice 2: Step 2. Find and graph discontinuities.

  36. Practice 2: Step 3. Use limits to determine behavior of graph around discontinuities.

  37. Practice 2: Step 4. Sketch a smooth curve.

  38. Practice 3: Step 1. Find and plot x and y intercepts.

  39. Practice 3: Step 1. Find and plot x and y intercepts.

  40. Practice 3: Step 2. Find and graph discontinuities.

  41. Practice 3: Step 3. Use limits to determine behavior of graph around discontinuities.

  42. Practice 3: Step 3. Use limits to determine behavior of graph around discontinuities.

  43. Practice 3: Step 4. Sketch a smooth curve.

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