# 4_3 - Chapter 4 Polynomial and Rational Functions 4.3 1 3...

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Chapter 4 446 Polynomial and Rational Functions 4.3 Rational Functions I 1. True 2. Quotient: 3 x - 6; Remainder: 6 x - 10 3. y = 1 x 4. True 5. y = 1 6. x = - 1 7. proper 8. False 9. True 10. True 11. In R ( x ) = 4 x x - 3 , the denominator, q ( x ) = x - 3, has a zero at 3. Thus, the domain of R ( x ) is x x 3 { } . 12. In R ( x ) = 5 x 2 3 + x , the denominator, q ( x ) = 3 + x , has a zero at –3. Thus, the domain of R ( x ) is x x ≠ - 3 { } . 13. In H ( x ) = - 4 x 2 ( x - 2)( x + 4) , the denominator, q ( x ) = ( x - 2)( x + 4), has zeros at 2 and –4. Thus, the domain of H ( x ) is x x ≠ - 4, x 2 { } . 14. In G ( x ) = 6 ( x + 3)(4 - x ) , the denominator, q ( x ) = ( x + 3)(4 - x ) , has zeros at –3 and 4. Thus, the domain of G ( x ) is x x ≠ - 3, x 4 { } .

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Section 4.3 Rational Functions I 447 15. In F ( x ) = 3 x ( x - 1) 2 x 2 - 5 x - 3 , the denominator, q ( x ) = 2 x 2 - 5 x - 3 = (2 x + 1)( x - 3), has zeros at - 1 2 and 3. Thus, the domain of F ( x ) is x x ≠ - 1 2 , x 3 . 16. In Q ( x ) = - x (1 - x ) 3 x 2 + 5 x - 2 , the denominator, q ( x ) = 3 x 2 + 5 x - 2 = (3 x - 1)( x + 2), has zeros at 1 3 and - 2. Thus, the domain of Q ( x ) is x x ≠ - 2, x 1 3 . 17. In R ( x ) = x x 3 - 8 , the denominator, q ( x ) = x 3 - 8 = ( x - 2)( x 2 + 2 x + 4) , has a zero at 2. ( x 2 + 2 x + 4 has no real zeros.) Thus, the domain of R ( x ) is x x 2 { } . 18. In R ( x ) = x x 4 - 1 , the denominator, q ( x ) = x 4 - 1 = ( x - 1)( x + 1)( x 2 + 1), has zeros at –1 and 1. ( x 2 + 1 has no real zeros.) Thus, the domain of R ( x ) is x x ≠ - 1, x 1 { } . 19. In H ( x ) = 3 x 2 + x x 2 + 4 , the denominator, q ( x ) = x 2 + 4 , has no real zeros. Thus, the domain of H ( x ) is x x is a real number { } . 20. In G ( x ) = x - 3 x 4 + 1 , the denominator, q ( x ) = x 4 + 1, has no real zeros. Thus, the domain of G ( x ) is x x is a real number { } . 21. In R ( x ) = 3( x 2 - x - 6) 4( x 2 - 9) , the denominator, q ( x ) = 4( x 2 - 9) = 4( x - 3)( x + 3) , has zeros at 3 and –3. Thus, the domain of R ( x ) is x x ≠ - 3, x 3 { } . 22. In F ( x ) = - 2( x 2 - 4) 3( x 2 + 4 x + 4) , the denominator, q ( x ) = 3( x 2 + 4 x + 4) = 3( x + 2) 2 , has a zero at –2. Thus, the domain of F ( x x x ≠ - 2 { } . 23. (a) Domain: x x 2 { } ; Range: y y 1 { } (b) Intercept: (0, 0) (c) Horizontal Asymptote: y = 1 (d) Vertical Asymptote: x = 2 (e) Oblique Asymptote: none 24. (a) Domain: x x ≠ - 1 { } ; Range: y y 0 { } (b) Intercept: (0, 2) (c) Horizontal Asymptote: y = 0 (d) Vertical Asymptote: x = - 1 (e) Oblique Asymptote: none
Chapter 4 Polynomial and Rational Functions 448 25. (a) Domain: x x 0 { } ; Range: all real numbers (b) Intercepts: (–1, 0), (1, 0) (c) Horizontal Asymptote: none (d) Vertical Asymptote: x = 0 (e)

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## This homework help was uploaded on 04/07/2008 for the course MAC 1105 taught by Professor Any during the Spring '08 term at FIU.

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4_3 - Chapter 4 Polynomial and Rational Functions 4.3 1 3...

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