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Algebra 2 CP Name________________ Assignment: H11 Chapter 8 Test Review Graph each rational function. Determine (a) the equations of any vertical asymptotes, (b)the equations of any horizontal asymptotes (c) x-intercepts, (d) y-intercepts (e) Domain, (f) Range. Note: please state if none exist! 2 3 2 1. f x 2. f x x 1 x2 Vertical Asymptote: Vertical Asymptote: Horizontal Asymptote: Horizontal Asymptote: Domain: Domain: Range: Range: x-Intercept: x-Intercept: y-intercept: y-intercept: 3. f x 3x 2 x2 1 4. f x x2 1 x Vertical Asymptote: Vertical Asymptote: Horizontal Asymptote: Horizontal Asymptote: Domain: Domain: Range: Range: x-Intercept: x-Intercept: y-intercept: y-intercept: 5. f x 5 x 4x 3 2 6. f x 12 4 x4 Vertical Asymptote: Vertical Asymptote: Horizontal Asymptote: Horizontal Asymptote: Domain: Domain: Range: Range: x-Intercept: x-Intercept: y-intercept: y-intercept: 7. f ( x) x x 1 2 Vertical Asymptote: Horizontal Asymptote: Domain: Range: x-Intercept: y-intercept: Simplify each expression. 3 24b 3 10bc 8. 5c 2 8b 5c 11. 16 y 2 40 y 25 4y 5 2 2 3 y 10 y 8 y 8 y 16 9. 3a 2 3a 2 a2 a 4 12. 10. x 2 19 x 84 2x 2 2 4x 4 x 9 x 14 x 3 13. x 1 2 14. x 2 100 x2 15. 2 3 x 31x 10 2x n4 16. n 2 6n 9 n 2n 8 3 n 2 32 x 4 y 8 xy2 3 xy2 21 y 4 x x 1 x 1 2 2 2 17. 16 2 x 16 x 4 18. 5 7 6ab 8a 19. 2 5m 4 m 5 m9 9m 20. 1 3 7 5n 4 10n 21. 2m 3 5 2 m 5m 6 m 9 22. x2 x 2 x x 12 x 2 x 3 2 2 Solve each equation or inequality. x 2 2x 4 23. x 3 2 24. 5 3 7 a a 25. x x 1 x 1 2 27. 2 x2 x2 x3 x6 x2 4 x 2 29. 2 x 4 x2 x2 26. 4 1 1 p 3p 5 28. 4v 5v 2 2 v 1 v2 v 3v 2 30. x 2 x 2 20 2x 1 2x 1 4x2 1 ANSWERS 1. VA: x = 1 HA: y = 0 D: x ≠ 1 R: y ≠ 0 x-int: None y-int: (0, -2) 2. VA: x = -2 HA: y = 2 D: x ≠ -2 R: y ≠ 2 x-int: (-1/2, 0) y-int: (0, 1/2) 3. VA: x = ±1 HA: y = 3 D: x ≠ ±1 R: y > 3 and y ≤ 0 x-int: (0, 0) y-int: (0, 0) 4. VA: x = 1 HA: None D: x ≠ 1 R: y ≥ 0 and y ≤ -4 x-int: (0, 0) y-int: (0, 0) 5. VA: x = 3,1 HA: y = 0 D: x ≠ 3, 1 R: y > 0 and y ≤ -5 x-int: None y-int: (0, 5/3) 6. VA: x = 4 HA: y = 4 D: x ≠ 4 R: y ≠ 4 x-int: (1, 0) y-int: (0, 1) 7. VA: x = ±1 HA: y = 0 D: x ≠ ±1 R: ARN x-int: (0, 0) y-int: (0, 0) 8. 6b 13. 9. a(a-2) 26 x 32 x 20 21b 24ab 17. 2 x4 21. 2m 2 2m 1 m 3m 3m 2 24. a = 2 29. No Solution 18. 25. x = 2, -1 10. 28x2y 11. 14. 23x 2 2 x x 1 15. 19. 9m 7 m9 22. 2 x 1x 2 x 4x 3x 1 20. 4 y 5 y 4 3y 2 2 x 10 x3 x 1 x 12 2x 2 16. 1 n 2n 3 36 5n 20n 23. -2, 3 2 26. p = 65 27. x = 14 3 3 30. x = 6, -3 12. 28. v = -2, -1