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Unformatted text preview: Section 6.1 Polynomial Functions 559 Version: Fall 2007 6.1 Exercises In Exercises 1 8 , arrange each polyno mial in descending powers of x , state the degree of the polynomial, identify the lead ing term, then make a statement about the coe ffi cients of the given polynomial. 1. p ( x ) = 3 x x 2 + 4 x 3 2. p ( x ) = 4 + 3 x 2 5 x + x 3 3. p ( x ) = 3 x 2 + x 4 x 4 4. p ( x ) = 3 + x 2 x 3 + 5 x 4 5. p ( x ) = 5 x 3 2 x 3 + 4 2 3 x 5 6. p ( x ) = 3 2 x + 5 7 3 x 5 + 4 3 x 3 7. p ( x ) = x + 2 3 x 3 √ 2 x 2 + π x 6 8. p ( x ) = 3+ √ 2 x 4 + √ 3 x 2 x 2 + √ 5 x 6 In Exercises 9 14 , you are presented with the graph of y = ax n . In each case, state whether the degree is even or odd, then state whether a is a positive or negative number. 9. x 5 y 5 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 10. x 5 y 5 11. x 5 y 5 12. x 5 y 5 560 Chapter 6 Polynomial Functions Version: Fall 2007 13. x 5 y 5 14. x 5 y 5 In Exercises 15 20 , you are presented with the graph of the polynomial p ( x ) = a n x n + · · · + a 1 x + a . In each case, state whether the degree of the polynomial is even or odd, then state whether the lead ing coe ffi cient a n is positive or negative. 15. x y 16. x y 17. x y 18. x y Section 6.1 Polynomial Functions 561 Version: Fall 2007 19. x y 20. x y For each polynomial in Exercises 21 30 , perform each of the following tasks. i. Predict the endbehavior of the poly nomial 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 endbehavior. ii. Draw the graph on your calculator, adjust the viewing window so that all "turning points" of the polyno mial are visible in the viewing win dow, and copy the result onto your homework paper. As usual, label and scale each axis with xmin, xmax, ymin, and ymax. Does the actual endbehavior agree with your predicted endbehavior? 21. p ( x ) = 3 x 3 + 2 x 2 + 8 x 4 22. p ( x ) = 2 x 3 3 x 2 + 4 x 8 23. p ( x ) = x 3 + x 2 17 x + 15 24. p ( x ) = x 4 + 2 x 2 + 29 x 30 25. p ( x ) = x 4 3 x 2 + 4 26. p ( x ) = x 4 + 8 x 2 12 27. p ( x ) = x 5 + 3 x 4 x 3 + 2 x 28. p ( x ) = 2 x 4 3 x 3 + x 10 29. p ( x ) = x 6 4 x 5 + 27 x 4 + 78 x 3 + 4 x 2 + 376 x 480 30. p ( x ) = x 5 27 x 3 +30 x 2 124 x +120 Chapter 6 Polynomial Functions Version: Fall 2007 6.1 Solutions 1. p ( x ) = x 3 x 2 + 3 x + 4 , degree = 3 , leading term = x 3 , " p is a polynomial with integer coe ffi cients," " p is a polynomial with rational coe ffi cients," or " p is a polynomial with real coe ffi cients." 3. p ( x ) = x 4 + 3 x 2 x 4 , degree = 4 , leading term = x 4 , " p is a polynomial with integer coe ffi cients," " p is a polynomial with rational coe ffi cients," or " p is a polynomial with real coe ffi cients." 5. p ( x ) = 2 3 x 5 3 2 x 3 + 5 x + 4 , degree = 5 , leading term = 2 3 x 5 , " p is a polynomial with rational coe...
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 polynomial functions, Extrema and Models

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