1 / 47

Homework, Page 234

Homework, Page 234. Write the polynomial in standard form, and identify the zeros of the function and the x -intercepts of its graph. 1. . Homework, Page 234. Write a polynomial function in minimum degree in standard form with real coefficients whose zeros include those listed. 5. .

brigette-abdiel
Download Presentation

Homework, Page 234

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Homework, Page 234 Write the polynomial in standard form, and identify the zeros of the function and the x-intercepts of its graph. 1.

  2. Homework, Page 234 Write a polynomial function in minimum degree in standard form with real coefficients whose zeros include those listed. 5.

  3. Homework, Page 234 Write a polynomial function in minimum degree in standard form with real coefficients whose zeros include those listed. 9.

  4. Homework, Page 234 Write a polynomial function in minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 13.

  5. Homework, Page 234 Match the polynomial function graph to the given zeros and multiplicities. 17. b.

  6. Homework, Page 234 State how many complex and real zeroes the function has. 21.

  7. Homework, Page 234 State how many complex and real zeroes the function has. 25. From the graph, f has four complex zeros, two of which are real.

  8. Homework, Page 234 Find all zeros and write a linear factorization of the function. 29.

  9. Homework, Page 234 Using the given zero, find all of the zeros and write a linear factorization of f (x). 33.

  10. Homework, Page 234 Write the function as a product of linear and irreducible quadratic factors all with real coefficients. 37.

  11. Homework, Page 234 Write the function as a product of linear and irreducible quadratic factors all with real coefficients. 41.

  12. Homework, Page 234 Answer Yes or No. If yes, give an example; if no, give a reason. 45. Is it possible to find a polynomial of degree 3 with real number coefficients that has -2 as its only real zero. Yes, for example

  13. Homework, Page 234 Find the unique polynomial with real coefficients that meets these conditions. 49. Degree 4; zeros at x = 3, x = –1, and x = 2 – i; f (0) = 30

  14. Homework, Page 234 53. There is at least one polynomial with real coefficients with 1 – 2i as its only nonreal zero. Justify your answer. False, to have real coefficients, the nonreal factors of a polynomial must be in conjugate pairs.

  15. Homework, Page 234 57. Which of the following cannot be the number of nonreal zeros of a polynomial of degree 5 with real coefficients? a. 0 b. 2 c. 3 d. 4 e. None of the above.

  16. Homework, Page 234 61. Verify that the complex number i is a zero of the polynomial

  17. Homework, Page 234 65. Find the three cube roots of 8 by solving

  18. 2.6 Graphs of Rational Functions

  19. Quick Review

  20. Quick Review Solutions

  21. What you’ll learn about • Rational Functions • Transformations of the Reciprocal Function • Limits and Asymptotes • Analyzing Graphs of Rational Functions … and why Rational functions are used in calculus and in scientific applications such as inverse proportions.

  22. Rational Functions

  23. Limits • We used limits to investigate continuity in Chapter 1 • Limits may also be used • to investigate behavior near vertical asymptotes • to investigate behavior as functions approach positive or negative infinity, usually called end behavior

  24. Transformations of the Reciprocal Function The general form for a function is In this equation, k indicates units of vertical translation, h indicates units of horizontal translation, and a indicates factor of stretch. For instance, indicates the reciprocal function is translated 4 units left and 3 down and stretched by a factor of 3.

  25. Example Finding the Domain of a Rational Function

  26. Graph a Rational Function

  27. Graph a Rational Function (Cont’d)

  28. Example Finding Asymptotes of Rational Functions

  29. Example Graphing a Rational Function

  30. Analyzing Graphs Use limits to describe the behavior of the function

  31. Finding Properties of Graphs Find the intercepts, vertical asymptotes, end behavior asymptotes, and graph the function.

  32. Homework • Review Section: 2.6 • Page 245, Exercises: 1 – 69 (EOO)

  33. 2.7 Solving Equations in One Variable

  34. Quick Review

  35. Quick Review Solutions

  36. 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.

  37. 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.

  38. Example Solving by Clearing Fractions

  39. Example Solving a Rational Function

  40. Example Eliminating Extraneous Solutions

  41. Example Eliminating Extraneous Solutions

  42. Example Finding an Acid Solution

  43. Example Finding an Acid Solution

  44. Example Finding an Acid solution

  45. Example Finding an Acid Solution

  46. Example Finding a Minimum Perimeter

  47. Example Finding a Minimum Perimeter

More Related