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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 \to \infty and x \to -\infty

1. f(x)=x^{4}

2. f(x)=x^{6}

3. f(x)=x^{3}

4. f(x)=x^{5}

5. f(x)=-x^{2}

6. f(x)=-x^{4}

7. f(x)=-x^{7}

8. f(x)=-x^{9}

Find the degree and leading coefficient of each polynomial

9. 4x^{7}

10. 5x^{6}

11. 5-x^{2}

12. 6+3x-4x^{3}

13. -2x^{4} - 3x^{2} + x-1

14. 6x^{5} -2x^{4} + x^{2} + 3

15. (2x+3)(x-4)(3x+1)

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

Find the long run behavior of each function as x \to \infty and x \to -\infty

17. -2x^{4} - 3x^{2} + x-1

18. 6x^{5} -2x^{4} + x^{2} + 3

19. 3x^{2} + x-2

20. -2x^{3} + x^{2} -x+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(t-1)(t+2)(t-3)

32. f(x)=3(x+1)(x-4)(x+5)

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

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

Answer

1. As x \to \infty, f(x) \to \infty As x \to -\infty, f(x) \to \infty

3. As x \to \infty, f(x) \to \infty As x \to -\infty, f(x) \to -\infty

5. As x \to \infty, f(x) \to -\infty As x \to -\infty, f(x) \to -\infty

7. As x \to \infty, f(x) \to -\infty As x \to -\infty, f(x) \to \infty

9. 7^{\text{th}} Degree, Leading coefficient 4

11. 2^{\text{nd}} Degree, Leading coefficient -1

13. 4^{\text{th}} Degree, Leading coefficient -2

15. 3^{\text{rd}} Degree, Leading coefficient 6

17. As x \to \infty, f(x) \to -\infty As x \to -\infty, f(x) \to -\infty

19. As x \to \infty, f(x) \to \infty As x \to -\infty, f(x) \to \infty

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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