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Pre-Calculus, Unit 3, Rational Functions Test Name: _________________________ Date: ____________ 1. Graph the function. Label all asymptotes. State the domain and range. (6 points) f ( x) 6 x 2x 1 Domain: ________________ Range: ________________ For 2 – 4, give the vertical, horizontal, and oblique asymptotes. If there is no asymptote, write “NONE.” 4 2. y 2 x 2 (6 points each) 2. VA: ________________ HA: ________________ OA: ________________ 3. y x2 4 x 2 8 x 15 3. VA: ________________ HA: ________________ OA: ________________ 4. 4. VA: ________________ HA: ________________ OA: ________________ Perform the indicated operation and simplify. (4 points each) 5. 3x 2 y 6 y 2 6. 4 x3 y 5 2 xy 3 5. ________________ 6. ________________ 7. x 6 2 x 5 x x 20 8. 3x x3 2 x 2 x 4 x 12 7. ________________ 8. ________________ Simplify. (4 points each) 9. 2x x3 x5 4 x 12 10. x5 10 x 2 3 3 5 x 9. ________________ 15 x 16 x 4 11. _______________ 10. _______________ Solve. (5 points each) 11. 8 5 x3 x3 12. 12. _______________ 13. 2x 1 x3 14. 13. _______________ 14. _______________ 15. You have subscribed to a cable television service. The cable company charges you a one-time installation fee of $30 and a monthly fee of $50. Write and graph a model that gives the average cost per month as a function of the number of months you have subscribed to the service. After how many months will the average cost be $53? (10 points) Equation: _______________ Number of months: _______________ 16. What function is graphed? (4 points) 20 A. y 10 x 119 x 12 B. y 10 x 121 x 12 C. y 10 x 119 x 12 D. y 10 x 121 x 12 18 16 14 12 10 8 6 4 E. None of these 2 5 17. What are all the solutions of the equation 10 15 20 6 x ? (4 points) x7 2 A. -4 B. -3 C. -4, -3 D. -3, 4 E. 3, 4 18. If , find On the same grid, graph (6 points) and Domain: Range: Domain: Range: 19. Write the partial fraction decomposition for: 3x . (8 points) x 4 2