1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 245 Find the domain of the function f. Use limits to describe the behavior of f at (near) values not in its domain. 1.

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 2 Homework, Page 245 Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function. Identify the vertical and horizontal asymptotes and use limits to describe corresponding behavior. Sketch the graph of f. 5. Translate the reciprocal function 3 units right.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 3 Homework, Page 245 Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function. Identify the vertical and horizontal asymptotes and use limits to describe corresponding behavior. Sketch the graph of f. 9. Translate the reciprocal function 4 units left and 2 units down.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 4 Homework, Page 245 Evaluate the limit based on the graph of f shown. 13.

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 5 Homework, Page 245 Evaluate the limit based on the graph of f shown. 17. [–9.8, 9] by [–5, 15]

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 6 Homework, Page 245 Find the horizontal and vertical asymptotes of f (x). Use limits to describe the corresponding behavior. 21.

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 7 Homework, Page 245 Find the asymptotes of the function, and graph the function. 25.

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 8 Homework, Page 245 Find the asymptotes of the function, and graph the function. 29.

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 9 Homework, Page 245 Find the asymptotes of the function, and graph the function. 33. a. Viewing window [-3,5] by [-5,10] with scale one on each axis

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 10 Homework, Page 245 Find the intercepts, asymptotes, use limits to describe the behavior at vertical asymptotes, and analyze and draw the graph of the given rational function. 37.

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 11 Homework, Page 245 Find the intercepts, asymptotes, use limits to describe the behavior at vertical asymptotes, and analyze and draw the graph of the given rational function. 41.

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 12 Homework, Page 245 Find the end-behavior asymptote of the given rational function and graph it together with f in two windows: a) One showing the details around the vertical asymptotes of f. b) One showing a graph of f that resembles its end-behavior asymptote. 45.

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 13 Homework, Page 245 Find the end-behavior asymptote of the given rational function and graph it together with f in two windows: a) One showing the details around the vertical asymptotes of f. b) One showing a graph of f that resembles its end-behavior asymptote. 49.

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 14 Homework, Page 245 Find the intercepts, analyze, and draw the graph of the given rational function. 53.

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 15 Homework, Page 245 Find the intercepts, asymptotes, end-behavior asymptote, and graph the function together with its end-behavior asymptote. 57.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 16 Homework, Page 245 Find the intercepts, asymptotes, end-behavior asymptote, and graph the function together with its end-behavior asymptote. 61.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 17 Homework, Page 245 65. Let. What values of x have to be excluded from the domain of f ? A. Only 0 B. Only 3 C. Only –3 D. Only 0, 3 E. Only 0, –3

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 18 Homework, Page 245 69. A. Are the domains equal? B. Does f have a vertical asymptote? Explain. The graph of f does not have a vertical asymptote because x – 3 is a factor of the numerator. C. Explain why the graphs appear to be identical. The graphs appear identical because the only difference is a removable discontinuity at x = 3 for the graph of f.

19. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 19 Homework, Page 245 69. D. Are the functions identical? The functions are not identical because f is discontinuous at x = 3 and g is continuous for all x.

20. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2.7 Solving Equations in One Variable

21. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 21 Quick Review

22. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 22 Quick Review Solutions

23. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 23 What you’ll learn about Solving Rational Equations Extraneous Solutions Applications … and why Applications involving rational functions as models often require that an equation involving fractions be solved.

24. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 24 Extraneous Solutions When we multiply or divide an equation by an expression containing variables, the resulting equation may have solutions that are not solutions of the original equation. These are extraneous solutions. For this reason we must check each solution of the resulting equation in the original equation.

25. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 25 Example Solving by Clearing Fractions

26. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 26 Example Solving a Rational Function

27. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 27 Example Eliminating Extraneous Solutions

28. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 28 Example Eliminating Extraneous Solutions

29. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 29 Example Finding an Acid Solution

30. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 30 Example Finding an Acid Solution

31. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 31 Example Finding an Acid solution

32. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 32 Example Finding an Acid Solution

33. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 33 Example Finding a Minimum Perimeter

34. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 34 Example Finding a Minimum Perimeter

35. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 35 Homework Review section 2.7 Page 253, Exercises: 1 – 53 (EOO)

36. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2.8 Solving Inequalities in One Variable

37. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 37 Quick Review

38. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 38 Quick Review Solutions

39. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 39 What you’ll learn about Polynomial Inequalities Rational Inequalities Other Inequalities Applications … and why Designing containers as well as other types of applications often require that an inequality be solved.

40. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 40 Polynomial Inequalities

41. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 41 Example Finding where a Polynomial is Zero, Positive, or Negative

42. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 42 Example Solving a Polynomial Inequality Analytically

43. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 43 Example Solving a Polynomial Inequality Graphically

44. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 44 Example Creating a Sign Chart for a Rational Function

45. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 45 Example Solving an Inequality Involving a Rational Function

46. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 46 Example Solving an Inequality Involving a Radical

47. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 47 Example Solving an Inequality Involving an Absolute Value