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Name:______________________________________ Chapter 8 Test Review Write a function that models each variation. 1. x = 1 when y = 5. y varies inversely as x. 2. x = 3 and y = 12 when z = 2. z varies directly with y and inversely with x. For each rational function, identify any holes and asymptotes (horizontal or vertical) of its graph. Also give the domain and range of each function. 3. y x x 3 4. x 2 5x 6 x 2 3x 2 Holes: Holes: VA: VA: HA: HA: Domain: Domain: Range: Range: 5. y x3 x 2 x 3 6. y Holes: Holes: VA: VA: HA: HA: Domain: Domain: Range: Range: 7. y = x 2 – 36 x+1 8. y 1 3 x4 x – 2 x + 4 x + 2 x – 3 Holes: Holes: VA: VA: HA: HA: Domain: Domain: Range: Range: Name:______________________________________ Sketch the graph of each rational function. x 9. 10. y x x 2 y 1 3 x4 VA: VA: Holes: Holes: HA: HA: X intercepts: X intercepts: Domain: Domain: Range: Range: Simplify each rational expression. 3 x 2 12 11. x2 x 6 13. 2 x x5 x5 12. 2 x2 x x 4 x2 4 x 1 8x 4 14. 3x 1 2 x 4 x 2 Name:______________________________________ 15. 17. 19. 16. y y – y– 1 y – 2 x y 2x – y 18. x+y 2x + y x 4 x 2 2 x 2x 8 x 16 2 2 3 3 1 4 3 1 20. x 2 + 2x – 15 x2 – 4 x– 3 2 4 x 10y 4 5 y 24 x3 1 x 1 5 y 1 21. Name:______________________________________ Solve each equation. Check each solution. 22. 24. x x 10 3 2 9 3 3 + = 28 x + 2 4 23. y 3 y 1 5 7 25. x + x2 – 5 x2 + x + 2 = x 2 –1 x+1