By S. Waner, S. Costenoble

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X y −1 x −1 21. x3 x4 22. y5 y3 23. x 2 y2 x −1 y 24. x −1 y x 2 y2 25. (x y −1 z 3 ) 2 x 2 yz 2 26. x 2 yz 2 (x yz −1 ) −1 27. 28. x 2 y −1 z 0 x yz −2 30. 61. 12. 3 · (−2) 0 17. x 3 x 2 x −1 y −2 z 2 xy 58. 11. 2 · 30 Simplify each expression in Exercises 17–30, expressing your answer in rational form. 29. √ a 2 b2 x y −2 z x −1 z x y −2 x 2 y −1 z 2 x2 71. √ x 2 74. −3 5x 76. 31. 1x −2 + 36. −4 3x 3 34. −3 78. 1 3 32. x −4 33. 3 35. 1 − −2 − x −1 x 5 Evaluate the expressions in Exercises 37–56, rounding your answer to four signiﬁcant digits where necessary.

4. Continuing, we get the following table. Chapter 1 Tools Function Evaluator & Grapher to ﬁnd a utility you can use to evaluate functions like this. 6 10 7 Sometimes, as in Example 4, we need to use several formulas to specify a single function. 3 One reason that more complex formulas are often less realistic than simple ones is that it is often random phenomena in the real world, rather than algebraic relationships, that cause data to ﬂuctuate. Attempting to model these random ﬂuctuations using algebraic formulas amounts to imposing mathematical structure where structure does not exist.

A. f (0) 2. ● a. f (−1) b. f (2) 8. ● Given g(x) = 2x 2 − x + 1, ﬁnd a. g(0) b. g(−1) c. g(r) d. g(x + h) 1 9. ● Given g(s) = s 2 + , ﬁnd a. g(1) b. g(−1) s c. g(4) d. g(x) e. g(s + h) f . g(s + h) − g(s) 1 10. ● Given h(r) = , ﬁnd a. h(0) b. h(−3) r +4 c. h(−5) b. f (1) 3. ● a. f (2) − f (−2) b. f (−1) f (−2) 4. ● a. f (1) − f (−1) b. f (1) f (−2) c. −2 f (−1) c. 3 f (−2) 5. ● Given f (x) = 4x − 3, ﬁnd a. f (−1) b. f (0) c. f (1) d. f ( y) e. f (a + b) hint [see Example 2] ● basic skills b. f (0) d.