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3.3E: Graphs of Polynomial Functions (Exercises)

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section 3.3 exercise

Find the C and t intercepts of each function.

1. C(t)=2(t4)(t+1)(t6)

2. C(t)=3(t+2)(t3)(t+5)

3. C(t)=4t(t2)2(t+1)

4. C(t)=2t(t3)(t+1)2

5. C(t)=2t48t3+6t2

6. C(t)=4t4+12t340t2

Use your calculator or other graphing technology to solve graphically for the zeros of the function.

7. f(x)=x37x2+4x+30

8. g(x)=x36x2+x+28

Find the long run behavior of each function as t and t

9. h(t)=3(t5)3(t3)3(t2)

10. k(t)=2(t3)2(t+1)3(t+2)

11. p(t)=2t(t1)(3t)2

12. q(t)=4t(2t)(t+1)3

Sketch a graph of each equation.

13. f(x)=(x+3)2(x2)

14. g(x)=(x+4)(x1)2

15. h(x)=(x1)3(x+3)2

16. k(x)=(x3)3(x2)2

17. m(x)=2x(x1)(x+3)

18. n(x)=3x(x+2)(x4)

Solve each inequality.

19. (x3)(x2)2>0

20. (x5)(x+1)2>0

21. (x1)(x+2)(x3)<0

22. (x4)(x+3)(x+6)<0

Find the domain of each function.

23. f(x)=42+19x2x2

24. g(x)=2817x3x2

25. h(x)=45x+x2

26. k(x)=2+7x+3x2

27. n(x)=(x3)(x+2)2

28. m(x)=(x1)2(x+3)

29. p(t)=1t2+2t8

30. q(t)=4x24x5

Write an equation for a polynomial the given features.

31. Degree 3. Zeros at x = -2, x = 1, and x = 3. Vertical intercept at (0, -4)

32. Degree 3. Zeros at x = -5, x = -2, and x = 1. Vertical intercept at (0, 6)

33. Degree 5. Roots of multiplicity 2 at x = 3 and x = 1, and a root of multiplicity 1 at x = -3. Vertical intercept at (0, 9)

34. Degree 4. Root of multiplicity 2 at x = 4, and a roots of multiplicity 1 at x = 1 and x = -2. Vertical intercept at (0, -3)

35. Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (2, 15)

36. Degree 5. Single zero at x = -2 and x = 3, and triple zero at x = 1. Passes through the point (2, 4)

Write a formula for each polynomial function graphed.

37. 屏幕快照 2019-06-23 上午3.24.15.png38. 屏幕快照 2019-06-23 上午3.24.35.png39.屏幕快照 2019-06-23 上午3.24.57.png

40. 屏幕快照 2019-06-23 上午3.25.18.png41. 屏幕快照 2019-06-23 上午3.25.44.png42. 屏幕快照 2019-06-23 上午3.26.12.png

43. 屏幕快照 2019-06-23 上午3.26.29.png44.屏幕快照 2019-06-23 上午3.26.46.png

Write a formula for each polynomial function graphed.

45. 屏幕快照 2019-06-23 上午5.32.03.png46.屏幕快照 2019-06-23 上午5.32.31.png

47. 屏幕快照 2019-06-23 上午5.32.47.png48. 屏幕快照 2019-06-23 上午5.33.17.png

49.屏幕快照 2019-06-23 上午5.33.39.png 50. 屏幕快照 2019-06-23 上午5.34.00.png

51. A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y=5x2. What are the dimensions of such a rectangle that has the greatest possible area?

52. A rectangle is inscribed with its base on the x axis and its upper corners on the curve y=16x4. What are the dimensions of such a rectangle that has the greatest possible area?

Answer
C(t) C, intercepts t, intercepts
1. (0, 48) (4, 0), (-1, 0), (6, 0)
3. (0, 0) (0, 0), (2, 0), (-1, 0)
5. (0, 0) (0, 0), (1, 0), (3, 0)

7. (-1.646, 0) (3.646, 0) (5, 0)

9. As t, h(t) t, h(t)

11. As t, p(t) t, p(t)

13. Screen Shot 2019-10-03 at 6.05.35 PM.png

15. Screen Shot 2019-10-03 at 6.05.54 PM.png

17. Screen Shot 2019-10-03 at 6.06.33 PM.png

19. (3,)

21. (,2)(1,3)

23. [3, 5, 6]

25. (,1][4,)

27. [2,2][3,)

29. (,4)(4,2)(2,)

31. y=23(x+2)(x1)(x3)

33. y=13(x1)2(x3)2(x+3)

35. y=15(x1)2(x3)2

37. y=12(x+2)(x1)(x3)

39. y=(x+1)2(x2)

41. y=124(x+3)(x+2)(x2)(x4)

43. y=124(x+4)(x+2)(x3)2

45. y=112(x+2)2(x3)2

47. y=16(x+3)(x+2)(x1)3

49. y=116(x+3)(x+1)(x2)2(x4)

51. Base 2.58, Height 3.336


This page titled 3.3E: Graphs of Polynomial Functions (Exercises) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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