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562 Chapter 6 Polynomial Functions 6.1 Answers 1. p(x) = −x 3 −x 2 +3x+4, degree = 3, leading term = −x 3 , “p is a polynomial with integer coefficients,” “p is a polynomial with rational coefficients,” or “p is a polynomial with real coefficients.” 21. Note that the leading term −3x 3 (dashed) has the same end-behavior as the polynomial p. y 10 3. p(x) = x 4 + 3x 2 − x − 4, degree = 4, leading term = x 4 , “p is a polynomial with integer coefficients,” “p is a polynomial with rational coefficients,” or “p is a polynomial with real coefficients.” −10 x 10 5. p(x) = − 2 3 x5 − 3 2 x3 +5x+4, degree = 5, leading term = − 2 3 x5 , “p is a polynomial with rational coefficients,” or “p is a polynomial with real coefficients.” −10 p(x)=−3x 3 +2x 2 +8x−4 7. p(x) = πx 6 + 2 3 x3 − √ 2x 2 −x, degree = 6, leading term = πx 6 , “p is a polynomial with real coefficients.” 9. y = ax n , n odd, a < 0. 11. y = ax n , n even, a > 0. 23. Note that the leading term x 3 (dashed) has the same end-behavior as the polynomial p. y −70 p(x)=x 3 +x 2 −17x+15 13. y = ax n , n odd, a < 0. 15. odd, positive 17. even, negative x −10 10 19. odd, positive −70 Version: Fall 2007
Section 6.1 Polynomial Functions 563 25. Note that the leading term x 4 (dashed) has the same end-behavior as the polynomial p. 29. Note that the leading term −x 6 (dashed) has the same end-behavior as the polynomial p. y 10 p(x)=x 4 −3x 2 +4 y 5000 −10 x 10 x −10 10 −10 −5000 p 27. Note that the leading term −x 5 (dashed) has the same end-behavior as the polynomial p. y 15 x −10 10 −10 p(x)=−x 5 +3x 4 −x 3 +2x Version: Fall 2007
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