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Math 160

Math 160. 3.2 – Polynomial Functions and Their Graphs. A polynomial function of degree is a function that can be written in the form :. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners .

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Math 160

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  1. Math 160 3.2 – Polynomial Functions and Their Graphs

  2. A polynomial function of degree is a function that can be written in the form:

  3. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  4. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  5. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  6. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  7. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  8. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  9. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  10. Polynomial functions are continuous and smooth. That means no gaps, holes, cusps, or corners.

  11. The end behavior of a function means how the function behaves when or . For non-constant polynomial functions, the end behavior is either or . The highest degree term of a polynomial, called the ___________, determines its end behavior.

  12. The end behavior of a function means how the function behaves when or . For non-constant polynomial functions, the end behavior is either or . The highest degree term of a polynomial, called the ___________, determines its end behavior.

  13. The end behavior of a function means how the function behaves when or . For non-constant polynomial functions, the end behavior is either or . The highest degree term of a polynomial, called the ___________, determines its end behavior.

  14. The end behavior of a function means how the function behaves when or . For non-constant polynomial functions, the end behavior is either or . The highest degree term of a polynomial, called the ___________, determines its end behavior. leading term

  15. Ex 1. Determine the end behavior of the polynomial .

  16. Ex 1. Determine the end behavior of the polynomial .

  17. Ex 2. Determine the end behavior of the polynomial .

  18. Ex 2. Determine the end behavior of the polynomial .

  19. Note: Zeros of a polynomial correspond with factors, and visually mean -intercepts. ex: If , then since , we must have a factor of . Also, there will be an -intercept at .

  20. Note: Zeros of a polynomial correspond with factors, and visually mean -intercepts. ex: If , then since , we must have a factor of . Also, there will be an -intercept at .

  21. Note: Zeros of a polynomial correspond with factors, and visually mean -intercepts. ex: If , then since , we must have a factor of . Also, there will be an -intercept at .

  22. Graphing Polynomial Functions Factor to find zeros and plot -intercepts. Plot test points (before smallest -intercept, between -intercepts, and after largest -intercept). Determine end behavior. 4. Graph.

  23. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  24. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  25. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  26. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  27. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  28. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  29. Ex 3. Sketch the graph of . Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  30. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  31. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  32. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  33. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  34. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  35. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  36. Ex 4. Sketch the graph of. Be sure to show intercepts, test points (before smallest -intercept, between -intercepts, and after largest -intercept), and end behavior.

  37. Multiplicity For the polynomial , the factor has multiplicity ___, and the factor has multiplicity ___.

  38. Multiplicity For the polynomial , the factor has multiplicity ___, and the factor has multiplicity ___.

  39. Multiplicity For the polynomial , the factor has multiplicity ___, and the factor has multiplicity ___.

  40. Multiplicity If a factor has an ______ multiplicity, then the curve will ______________ the -axis at :

  41. Multiplicity If a factor has an ______ multiplicity, then the curve will ______________ the -axis at : odd

  42. Multiplicity If a factor has an ______ multiplicity, then the curve will ______________ the -axis at : odd pass through

  43. Multiplicity If a factor has an ______ multiplicity, then the curve will ______________ the -axis at :

  44. Multiplicity If a factor has an ______ multiplicity, then the curve will ______________ the -axis at : even

  45. Multiplicity If a factor has an ______ multiplicity, then the curve will ______________ the -axis at : even “bounce” off

  46. Ex 5. Based on the graph below, determine if the multiplicities of each zero of are even or odd.

  47. Ex 5. Based on the graph below, determine if the multiplicities of each zero of are even or odd.

  48. Ex 5. Based on the graph below, determine if the multiplicities of each zero of are even or odd.

  49. Ex 5. Based on the graph below, determine if the multiplicities of each zero of are even or odd.

  50. Ex 5. Based on the graph below, determine if the multiplicities of each zero of are even or odd.

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