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4.1E: Power Functions (Exercises)

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section 3.1 EXERCISE

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

1. f(x)=x4

2. f(x)=x6

3. f(x)=x3

4. f(x)=x5

5. f(x)=x2

6. f(x)=x4

7. f(x)=x7

8. f(x)=x9

Find the degree and leading coefficient of each polynomial

9. 4x7

10. 5x6

11. 5x2

12. 6+3x4x3

13. 2x43x2+x1

14. 6x52x4+x2+3

15. (2x+3)(x4)(3x+1)

16. (3x+1)(x+1)(4x+3)

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

17. 2x43x2+x1

18. 6x52x4+x2+3

19. 3x2+x2

20. 2x3+x2x+3

21. What is the maximum number of x-intercepts and turning points for a polynomial of degree 5?

22. What is the maximum number of x-intercepts and turning points for a polynomial of degree 8?

What is the least possible degree of the polynomial function shown in each graph?

23.屏幕快照 2019-06-22 上午10.45.33.png24屏幕快照 2019-06-22 上午10.45.56.png.25.屏幕快照 2019-06-22 上午10.46.26.png26.屏幕快照 2019-06-22 上午10.46.46.png

27. 屏幕快照 2019-06-22 上午10.47.08.png28.屏幕快照 2019-06-22 上午10.47.39.png29.屏幕快照 2019-06-22 上午10.48.00.png30. 屏幕快照 2019-06-22 上午10.48.27.png

Find the vertical and horizontal intercepts of each function.

31. f(t)=2(t1)(t+2)(t3)

32. f(x)=3(x+1)(x4)(x+5)

33. g(n)=2(3n1)(2n+1)

34. k(u)=3(4n)(4n+3)

Answer

1. As x, f(x) As x, f(x)

3. As x, f(x) As x, f(x)

5. As x, f(x) As x, f(x)

7. As x, f(x) As x, f(x)

9. 7th Degree, Leading coefficient 4

11. 2nd Degree, Leading coefficient -1

13. 4th Degree, Leading coefficient -2

15. 3rd Degree, Leading coefficient 6

17. As x, f(x) As x, f(x)

19. As x, f(x) As x, f(x)

21. intercepts: 5, turning points: 4

23. 3

25. 5

27. 3

29. 5

31. Horizontal Intercepts (1, 0), (-2, 0), (3, 0) Vertical Intercept (0, 12)

33. Horizontal Intercepts (1/3, 0) (-1/2. 0) Vertical Intercept (0, 2)


This page titled 4.1E: Power Functions (Exercises) is shared under a CC BY-SA license and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The OpenTextBookStore) .

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