1. Chapter 0 Review Calculus

2. Find the inequality that represents the graphed numbers. -6 < x < 5 Now write the interval notation: (-6, 5)

3. What is the interval notation of 3 < x ≤ 5 (3, 5]

4. Identify the notation that denotes the statement that “x is greater than 3 and no greater than 13” (3, 13]

5. Solve and graph: ]

6. ) Test around pts. 6 and -4 ( (-∞, -4) U (6, ∞)

7. Solve and graph: ]( (-3, -1]

8. Adrienne is planning a 4-hour hike, and is looking for a park within a reasonable distance from her house. She can drive at an average of 35 miles per hour, but she does not want to spend more than 6 hours away from home. Which describes the possible one-way distance Adrienne can travel from her home to the park?

9. Sean works weekends and earns $5.30 per hour after deductions. He wants at least $335 for a stereo system. What is the fewest hours he must work to reach this goal? 64 hours

10. The force F applied to an elevator cable by the total weight s of the elevator can be determined by, where F is in newtons. The sign in the elevator limits the total weight of passengers and baggage to 2,500 kilograms. The empty elevator weighs 1,100 kilograms. What inequality expresses the possible range of the force on the elevator cable in newtons (N)??

11. A company’s monthly cost C, in dollars, for storing x surplus units of a product is: Find the widest range of x values for which the monthly cost will not exceed $4,400

12. Katalin is on a mountain 11,033 feet above sea level. Nick is in a submarine 3414 feet below sea level. Which of the following can be used to find the difference between Katalin’s elevation and Nick’s elevation?

13. Find the distance between a and b, a = -9.7, b = 2 11.7

14. Find the directed distance from a to b, a = -9.2, b = -3.5 5.7

15. Write an absolute value inequality from the given information. (3, 8)

16. Write an absolute value inequality from the given information. (-∞, -3) U (4, ∞)

17. Mr. Williams sells jumbo-size bags of peanut butter chocolate chunk cookies. The number of cookies in each bag must not differ from 100 by more than 7 cookies. Find an inequality which describes b, the acceptable number of cookies in each bag.

18. For a cupboard door to meet specifications at a carpentry shop, the width must be within ⅛ inch of the expected width of the door. Find an inequality that expresses the range of acceptable widths for doors that are 2 feet wide, and find the minimum acceptable width of the doors.

19. Find the midpoint of the given interval: [2, 7]

20. Evaluate when x = -2

21. Evaluate when x = 3

22. Evaluate when x = 81

23. Evaluate when x = 9

24. Simplify:

28. Find the domain of the given expression.

30. Test around pts. and

31. Find the domain of the given expression. Test around pts. and

32. Find the complete factorization of the polynomial. Find the factors of 72 that add up to 22 18 and 4 Break up the middle term

33. Find the complete factorization of the polynomial.

34. Factoring doesn’t work, so let’s try synthetic division. Try all the possible rational roots.

35. Find the complete factorization of the polynomial. Sum of Cubes

36. Find the complete factorization of the polynomial. Difference of Squares

37. Find the interval on which the given expression is defined. Can’t have negative value under the square root sign Test points around -4 and -3 (-∞, -4] U [-3, ∞)

38. Find the interval on which the given expression is defined. Can’t have negative value under the square root sign Test points around -6 and -5 (-∞, -6] U [-5, ∞)

39. Find the domain of the given expression Can’t have negative value under the square root sign Test points around 2 and 5 [2, 5]

40. Find the interval on which the given expression is defined. Can’t have negative value under the square root sign Test points around

41. Use synthetic division to complete the indicated factorization.

45. Use the Rational Zero Theorem to determine all possible rational zeros of the polynomial. Do not find the actual zeros. PQ FACTORS OF “P”: ±1, ±3 FACTORS OF “Q”: ±1, ±3 “P over Q”

46. Use the Rational Zero Theorem to determine all possible rational zeros of the polynomial. Do not find the actual zeros. PQ FACTORS OF “P”: ±1, ±2, ±3, ±6 FACTORS OF “Q”: ±1, ±3 “P over Q”

47. Use the rational zero theorem as an aid in finding all the real zeros of the polynomial. FACTORS OF “P”: ±1, ±2, ±4, ±5, ±10, ±20 FACTORS OF “Q”: ±1 So 1 is a root So 1, -5, and 4 are roots

48. Use the rational zero theorem as an aid in finding all the real zeros of the polynomial. FACTORS OF “P”: ±1, ±2, ±3, ±5, ±6, ±10, ±15, ±30 FACTORS OF “Q”: ±1 So -2 is a root So 1, 5, and -3 are roots

49. Simplify a Rational Expression Factor the numerator and denominator. Divide both the numerator and denominator by the common factor, 2-x. The numerator and denominator are opposites, or additive inverses. They differ only in their signs. Factors that are OppositesEXAMPLE

50. Simplifying Rational ExpressionsEXAMPLE Simplify: SOLUTION Factor the numerator and denominator. Divide out the common factor, x + 1. Simplify.

51. Simplifying Rational ExpressionsEXAMPLE Simplify: SOLUTION Factor the numerator and denominator. Rewrite 3 – x as (-1)(-3 + x). Rewrite -3 + x as x – 3.

52. Simplifying Rational Expressions Divide out the common factor, x – 3. Simplify. CONTINUED

53. Factor the numerator and denominator. Divide both the numerator and denominator by the common factor, x-4. Simplifying Rational ExpressionsEXAMPLE

54. Simplify Assume the denominator cannot equal zero. Factor out a negative one to move things around

55. Simplify Assume the denominator cannot equal zero.

56. Simplify Assume the denominator cannot equal zero.

57. Multiply the fractions Reduce before multiply.

58. Multiply the fractions Reduce before multiply.

59. Multiply the fractions Reduce before multiply.

60. Simplify the Complex fraction Remember fractions are division statements.

61. Simplify the Complex fraction Remember fractions are division statements.

62. Simplify the Complex fraction

65. Simplify this expression:

72. ???? Missing a step?????

73. Rationalize the denominator:

74. Rationalize the numerator:

77. The Whole Process Rewrite numerators Make new denominators using LCD Make equivalent expressions Combine Expressions over One Denominator 3x 2 2x 5 2 5 6x 5 (2x 3 )(3) 4x 3 15 6x 5 + + + 4x 3 + 15

78. 4a 2 b 10ab 3 5 3 20a 2 b 3 (5b 2 )(2a) 20a 2 b 3 25b 2 6a - - - 20a 2 b 3 25b 2 – 6a

79. 5 2c + 1 6c 5 + 1 6c (3) 16 6c 8 3c

80. Polynomial Problems Factor all polynomials LCD is all the different “ numbers ” present x 2 – 4 x + 2 3 _ 1 (x + 2)(x – 2) (x + 2) 3 _ 1 (x + 2)(x – 2) (x – 2) (x + 2)(x – 2) 3 – 1(x – 2) (x + 2)(x – 2) -x + 5

81. 4 _ 5 3 x 4 _ 5 3x x(3) 3x 4x _ 15 4x – 15 3x

82. x + 2 4 x – 3 + + (x + 2) 4 x – 3 (x – 3) x – 3 + x 2 – x – 6 4 x 2 – x – 2 x – 3 (x + 1)(x – 2) x – 3

83. a 2 – 36 6 – a + 3 2 (a + 6)(a – 6) – 1(a – 6) + 3 2 3 _ 2 (a + 6)(a – 6) (a + 6) (a + 6)(a – 6) 3 – 2a – 12 (a + 6)(a – 6) - 2a - 9

84. 3x _ 5x x 9x + 2 2 – 9x 81x 2 – 4 + 3x 5x x 9x + 2 -1(9x – 2) (9x + 2)(9x – 2) _ + 3x 5x x + (9x + 2)(9x – 2) (9x + 2)(9x – 2) (9x + 2)(9x – 2) (9x – 2)(9x + 2) 27x 2 – 6x + 45x 2 + 10x + x (9x + 2)(9x – 2) 72x 2 + 5x