Chap6 Section1

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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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 coefficients 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 + πx 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: 1 10. x 5 y 5 11. x 5 y 5 12. x 5 y 5
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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 0 . In each case, state whether the degree of the polynomial is even or odd, then state whether the lead- ing coefficient a n is positive or negative. 15. x y 16. x y 17. x y 18. x y
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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 end-behavior 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 end-behavior. 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
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