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Exercises with Answers

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Section 6.1 Polynomial Functions 561

19.

y

21. p(x) = −3x 3 + 2x 2 + 8x − 4

22. p(x) = 2x 3 − 3x 2 + 4x − 8

23. p(x) = x 3 + x 2 − 17x + 15

x

24. p(x) = −x 4 + 2x 2 + 29x − 30

25. p(x) = x 4 − 3x 2 + 4

20.

y

26. p(x) = −x 4 + 8x 2 − 12

27. p(x) = −x 5 + 3x 4 − x 3 + 2x

28. p(x) = 2x 4 − 3x 3 + x − 10

29. p(x) = −x 6 − 4x 5 + 27x 4 + 78x 3 +

4x 2 + 376x − 480

x

30. p(x) = x 5 −27x 3 +30x 2 −124x+120

For each polynomial in Exercises 21-

30, perform each of the following tasks.

i. Predict the end-behavior of the polynomial

by drawing a very rough sketch

of the polynomial. Do this without

the assistance of a calculator. The

only concern here is that your graph

show the correct end-behavior.

ii. Draw the graph on your calculator,

adjust the viewing window so that

all “turning points” of the polynomial

are visible in the viewing window,

and copy the result onto your

homework paper. As usual, label and

scale each axis with xmin, xmax, ymin,

and ymax. Does the actual end-behavior

agree with your predicted end-behavior?

Version: Fall 2007

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560 Chapter 6 Polynomial Functions 13. 16. y 5 y x 5 x 14. 17. y 5 y x 5 x In Exercises 15-20, you are presented with the graph of the polynomial p(x) = a n x n + · · · + a 1 x + a 0 . In each case, state whether the degree of the polynomial is even or odd, then state whether the leading coefficient a n is positive or negative. 15. 18. y x y x Version: Fall 2007

Section 6.1 Polynomial Functions 561 19. y 21. p(x) = −3x 3 + 2x 2 + 8x − 4 22. p(x) = 2x 3 − 3x 2 + 4x − 8 23. p(x) = x 3 + x 2 − 17x + 15 x 24. p(x) = −x 4 + 2x 2 + 29x − 30 25. p(x) = x 4 − 3x 2 + 4 20. y 26. p(x) = −x 4 + 8x 2 − 12 27. p(x) = −x 5 + 3x 4 − x 3 + 2x 28. p(x) = 2x 4 − 3x 3 + x − 10 29. p(x) = −x 6 − 4x 5 + 27x 4 + 78x 3 + 4x 2 + 376x − 480 x 30. p(x) = x 5 −27x 3 +30x 2 −124x+120 For each polynomial in Exercises 21- 30, perform each of the following tasks. i. Predict the end-behavior of the polynomial by drawing a very rough sketch of the polynomial. Do this without the assistance of a calculator. The only concern here is that your graph show the correct end-behavior. ii. Draw the graph on your calculator, adjust the viewing window so that all “turning points” of the polynomial are visible in the viewing window, and copy the result onto your homework paper. As usual, label and scale each axis with xmin, xmax, ymin, and ymax. Does the actual end-behavior agree with your predicted end-behavior? Version: Fall 2007

Page 1: Section 6.1 Polynomial Functions 55
Page 5: Section 6.1 Polynomial Functions 56

Exercises with Answers

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