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# 4_2 - Chapter 4 Polynomial and Rational Functions 4.2 1 3 5...

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Chapter 4 415 Polynomial and Rational Functions 4.2 Polynomial Functions 1. (2, 0), (–2, 0), and (0, 9) 2. True 3. down, 4 4. True 5. smooth, continuous 6. zero or root 7. touches 8. True 9. False 10. False 11. f ( x ) = 4 x + x 3 is a polynomial function of degree 3. 12. f ( x ) = 5 x 2 + 4 x 4 is a polynomial function of degree 4. 13. g ( x ) = 1 - x 2 2 = 1 2 - 1 2 x 2 is a polynomial function of degree 2. 14. h ( x ) = 3 - 1 2 x is a polynomial function of degree 1. 15. f ( x ) = 1 - 1 x = 1 - x - 1 is not a polynomial function because it contains a negative exponent. 16. f ( x ) = x ( x - 1) = x 2 - x is a polynomial function of degree 2. 17. g ( x ) = x 3 / 2 - x 2 + 2 is not a polynomial function because it contains a fractional exponent. 18. h ( x ) = x x - 1 ( 29 = x - x is not a polynomial function because it contains a square root. 19. F ( x ) = 5 x 4 - π x 3 + 1 2 is a polynomial function of degree 4. 20. F ( x ) = x 2 - 5 x 3 = 1 x - 5 x 3 is not a polynomial function because it contains a variable with a positive exponent in the denominator.

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Chapter 4 Polynomial and Rational Functions 416 21. G ( x ) = 2 x - 1 ( 29 2 x 2 + 1 ( 29 = 2 x 2 - 2 x + 1 ( 29 x 2 + 1 ( 29 = 2 x 4 + x 2 - 2 x 3 - 2 x + x 2 + 1 ( 29 = 2 x 4 - 4 x 3 + 4 x 2 - 4 x + 2 is a polynomial function of degree 4. 22. G ( x ) = - 3 x 2 x + 2 ( 29 3 = - 3 x 2 x 3 + 6 x 2 + 12 x + 8 ( 29 = - 3 x 5 - 18 x 4 - 36 x 3 - 24 x 2 is a polynomial function of degree 5. 23. f ( x ) = ( x + 1) 4 Using the graph of y = x 4 , shift the graph horizontally, to the left 1 unit. 24. f ( x ) = ( x - 2) 5 Using the graph of y = x 5 , shift the graph horizontally to the right 2 units. 25. f ( x ) = x 5 - 3 Using the graph of y = x 5 , shift the graph vertically, down 3 units. 26. f ( x ) = x 4 + 2 Using the graph of y = x 4 , shift the graph vertically up 2 units.
Section 4.2 Polynomial Functions 417 27. f ( x ) = 1 2 x 4 Using the graph of y = x 4 , compress the graph vertically by a factor of 1 2 . 28. f ( x ) = 3 x 5 Using the graph of y = x 5 , stretch the graph vertically by a factor of 3. 29. f ( x ) = - x 5 Using the graph of y = x 5 , reflect the graph about the x- axis. 30. f ( x ) = - x 4 Using the graph of y = x 4 , reflect the graph about the x- axis. 31. f ( x ) = ( x - 1) 5 + 2 Using the graph of y = x 5 , shift the graph horizontally, to the right 1 unit, and shift vertically up 2 units. 32. f ( x ) = ( x + 2 ) 4 - 3 Using the graph of y = x 4 , shift the graph horizontally left 2 units, and shift vertically down 3 units.

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Chapter 4 Polynomial and Rational Functions 418 33. f ( x ) = 2( x + 1) 4 + 1 Using the graph of y = x 4 , shift the graph horizontally, to the left 1 unit, stretch vertically by a factor of 2, and shift vertically up 1 unit. 34. f ( x ) = 1 2 ( x - 1) 5 - 2 Using the graph of y = x 5 , shift the graph horizontally to the right 1 unit, compress vertically by a factor of 1 2 , and shift vertically down 2 units. 35. f ( x ) = 4 - ( x - 2) 5 = - ( x - 2) 5 + 4 Using the graph of y = x 5 , shift the graph horizontally, to the right 2 units, reflect about the x- axis, and shift vertically up 4 units. 36. f ( x ) = 3 - ( x + 2) 4 = - ( x + 2 ) 4 + 3 Using the graph of y = x 4 , shift the graph horizontally, to the left 2 units, reflect about the x- axis, and shift vertically up 3 units.
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4_2 - Chapter 4 Polynomial and Rational Functions 4.2 1 3 5...

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