Tutorials--Rational Expressions
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This document provides 28 examples of graphs of different types of rational functions. The rational functions shown include those of the form y=1/x, y=(x+a)/(x+b), y=-(x-a)/(x-b), and others with varying constants in both the numerator and denominator. Each example graphically depicts a different rational function to illustrate their key characteristics and behaviors.
![Example 12: The graph of a rational function of the form y = (x + a)/
[(x + b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-14-320.jpg)
![Example 13: The graph of a rational function of the form y = (x - a)/
[(x + b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-15-320.jpg)
![Example 14: The graph of a rational function of the form y = (x + a)/
[(x - b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-16-320.jpg)
![Example 15: The graph of a rational function of the form y = (x + a)/
[(x + b)(x - c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-17-320.jpg)
![Example 16: The graph of a rational function of the form y = (x - a)/
[(x - b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-18-320.jpg)
![Example 17: The graph of a rational function of the form y = (x - a)/
[(x + b)(x - c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-19-320.jpg)
![Example 18: The graph of a rational function of the form y = (x - a)/
[(x - b)(x - c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-20-320.jpg)
![Example 22: The graph of a rational function of the form y = -(x +
a)/[(x + b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-24-320.jpg)
![Example 23: The graph of a rational function of the form y = -(x -
a)/[(x + b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-25-320.jpg)
![Example 24: The graph of a rational function of the form y = -(x +
a)/[(x - b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-26-320.jpg)
![Example 25: The graph of a rational function of the form y = -(x +
a)/[(x + b)(x - c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-27-320.jpg)
![Example 26: The graph of a rational function of the form y = -(x -
a)/[(x - b)(x + c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-28-320.jpg)
![Example 27: The graph of a rational function of the form y = -(x -
a)/[(x + b)(x - c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-29-320.jpg)
![Example 28: The graph of a rational function of the form y = (x - a)/
[(x - b)(x - c)].](https://image.slidesharecdn.com/tutorials-rationalexpressions-130626212548-phpapp02/85/Tutorials-Rational-Expressions-30-320.jpg)
Tutorials--Rational Expressions
- 1. Graphs of Rational Functions
- 2. Overview This set of tutorials provides 28 examples of graphs of rational functions.
- 3. Example 1: The graph of a rational function of the form y = 1/x.
- 4. Example 2: The graph of a rational function of the form y = -1/x.
- 5. Example 3: The graph of a rational function of the form y = 1/(x + c).
- 6. Example 4: The graph of a rational function of the form y = 1/(x - c).
- 7. Example 5: The graph of a rational function of the form y = 1/(cx + d).
- 8. Example 6: The graph of a rational function of the form y = -1/(cx + d).
- 9. Example 7: The graph of a rational function of the form y = 1/(cx - d).
- 10. Example 8: The graph of a rational function of the form y = 1/(-cx + d).
- 11. Example 9: The graph of a rational function of the form y = (x + a)/ (x + b).
- 12. Example 10: The graph of a rational function of the form y = (x - a)/ (x + b).
- 13. Example 11: The graph of a rational function of the form y = (x - a)/ (x - b).
- 14. Example 12: The graph of a rational function of the form y = (x + a)/ [(x + b)(x + c)].
- 15. Example 13: The graph of a rational function of the form y = (x - a)/ [(x + b)(x + c)].
- 16. Example 14: The graph of a rational function of the form y = (x + a)/ [(x - b)(x + c)].
- 17. Example 15: The graph of a rational function of the form y = (x + a)/ [(x + b)(x - c)].
- 18. Example 16: The graph of a rational function of the form y = (x - a)/ [(x - b)(x + c)].
- 19. Example 17: The graph of a rational function of the form y = (x - a)/ [(x + b)(x - c)].
- 20. Example 18: The graph of a rational function of the form y = (x - a)/ [(x - b)(x - c)].
- 21. Example 19: The graph of a rational function of the form y = -(x + a)/(x + b).
- 22. Example 20: The graph of a rational function of the form y = -(x - a)/(x + b).
- 23. Example 21: The graph of a rational function of the form y = -(x - a)/(x - b).
- 24. Example 22: The graph of a rational function of the form y = -(x + a)/[(x + b)(x + c)].
- 25. Example 23: The graph of a rational function of the form y = -(x - a)/[(x + b)(x + c)].
- 26. Example 24: The graph of a rational function of the form y = -(x + a)/[(x - b)(x + c)].
- 27. Example 25: The graph of a rational function of the form y = -(x + a)/[(x + b)(x - c)].
- 28. Example 26: The graph of a rational function of the form y = -(x - a)/[(x - b)(x + c)].
- 29. Example 27: The graph of a rational function of the form y = -(x - a)/[(x + b)(x - c)].
- 30. Example 28: The graph of a rational function of the form y = (x - a)/ [(x - b)(x - c)].