394 CHAPTER 3 Polynomial and Rational Functions Concept Check Use the graphs of the rational functions in choices A–D to answer each question. There may be more than one correct choice. A. 3 3 0 x y B. 3 3 0 x y C. 3 3 0 x y D. 3 1 0 x y 9. Which choices have domain 1-∞, 32 ´13, ∞2? 10. Which choices have range 1-∞, 32 ´13, ∞2? 11. Which choices have range 1-∞, 02 ´10, ∞2? 12. Which choices have range 10, ∞2? 13. If ƒ represents the function, only one choice has a single solution to the equation ƒ1x2 = 3. Which one is it? 14. Which choices have domain 1-∞, 02 ´10, 32 ´13, ∞2? 15. Which choices have the x-axis as a horizontal asymptote? 16. Which choices are symmetric with respect to a vertical line? Explain how the graph of each function can be obtained from the graph of y = 1 x or y = 1 x2 . Then graph f and give the (a) domain and (b) range. Determine the largest open intervals of the domain over which the function is (c) increasing or (d) decreasing. See Examples 1–3. 17. ƒ1x2 = 2 x 18. ƒ1x2 = - 3 x 19. ƒ1x2 = 1 x + 2 20. ƒ1x2 = 1 x - 3 21. ƒ1x2 = 1 x + 1 22. ƒ1x2 = 1 x - 2 23. ƒ1x2 = - 2 x2 24. ƒ1x2 = 1 x2 + 3 25. ƒ1x2 = 1 1x - 322 26. ƒ1x2 = -2 1x - 322 27. ƒ1x2 = -1 1x + 222 - 3 28. ƒ1x2 = -1 1x - 422 + 2
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