By S. Waner, S. Costenoble

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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. h(x 2 ) −t 11. ● Given f (t) = t 2 t e. h(x 2 + 1) f . h(x 2 ) + 1 if t < 0 if 0 ≤ t < 4 if t ≥ 4 ﬁnd a.

X + y − x y) 2 32. y 2 − 4y 2 35. x 2 − 8x + 7 36. y 2 + 6y + 8 37. x 2 + x − 12 38. y 2 + y − 6 39. 2x 2 − 3x − 2 40. 3y 2 − 8y − 3 41. 6x + 13x + 6 42. 6y 2 + 17y + 12 43. 12x 2 + x − 6 44. 20y 2 + 7y − 3 45. x 2 + 4x y + 4y 2 46. 4y 2 − 4x y + x 2 47. x 4 − 5x 2 + 4 48. y 4 + 2y 2 − 3 2 21. ( y 3 + 2y 2 + y)( y 2 + 2y − 1) 22. (x 3 − 2x 2 + 4)(3x 2 − x + 2) In Exercises 23–30, factor each expression and simplify as much as possible. 34. 3y 3 − 9y 2 23. (x + 1)(x + 2) + (x + 1)(x + 3) 24. 4 Rational Expressions Rational Expression P , where P and Q are Q simpler expressions (usually polynomials) and the denominator Q is not zero.

Thus, the price of EBAY stock was $86 after 1 week, $70 after 5 weeks, and $80 after 10 weeks. com, November, 2004 The functions we used in Examples 1– 4 above are mathematical models of reallife situations, because they model, or represent, situations in mathematical terms. Mathematical Modeling To mathematically model a situation means to represent it in mathematical terms. The particular representation used is called a mathematical model of the situation. Mathematical models do not always represent a situation perfectly or completely.