55a

test 3

7.6

11. Solve for x. ( Hint: Isolate square root. Square both sides.)

The value for x is between

a 0 and 20

b 20 and 40

c 40 and 60

d 60 and 80

e nota

12. Solve for x . ( Hint: Square both sides.)

The value for x is between

a 0 and 2

b 2 and 4

c 4 and 6

d nota

13. Solve for x. ( Hints: Isolate square root. Square both sides. Isolate square root again. Square both sides again. )

The value of x is between

a -10 and 0

b 0 and 10

c 10 and 20

d nota

7.7

14.
Add: (4 - i) + ( 6 - 7i) (Hint: Collect like terms.)

a 8i - 10

b 8 - 10i

c 10 - 8i

d nota

15. Multiply

(4 - i)·( 6 - 7i)

Hint: Use FOIL and the fact that i² = -1.

a -17 -34i

b 17 - 34i

c 31 - 34i

d 17 + 34i

e nota

16. Divide
(4 - i)/( 6 + 7i)

a (17i - 34)/85

b (17 - 34i)/13

c (17 - 34i)/85

d nota

17.
Complete the square and factor:

x² - 8x
Hint: Divide -8 by 2 and square the result. Then add. Then factor.

a (x - 2)²

b (x - 4)²

c (x + 4)²

d (x + 8)²

e nota

8.3

18. What formula best corresponds to this picture ?

a f(x) = (x + 1)² + 1

b f(x) = (x - 1)² + 1

c f(x) =(x + 1)² - 1

d f(x) = - (x - 1)² + 1

e nota

19. What is the vertex (h,k) of this parabola ? (Hint: Complete the square and factor.)
f(x) = x² + 2x - 3

a (1,2)

b (-1,2)

c (0,3)

d (-1,-4)

e nota

20. What is the vertex (h,k) of this parabola ?
f(x) = 2x² + 4x - 3

Hint: Write as as 2·(x² + 2x ) - 3. Then complete the square inside the ( ).

a (1,2)

b (1,-2)

c (-1,-5)

d (0,3)

e nota

8.4

21. Solve for x. The ranges for the answers are below:

x⁴ - 5x² + 4 = 0

a {-2, 2, -1,1}

b {-2, 2, 1,1}

c {2, 2, -1,1}

d nota

8.5

22. Solve the inequality : x² + x - 6 < 0 .

(Hint: Factor the left hand side. Then make a number line for each factor. Make three regions I, II and III. )

a -3 < x < 2

b x < 2 or x > 3

c x < -3 or x > 2

d 2 < x < 3

e nota

23. Solve the inequality: (x + 3)/(x - 2) > 0 .
(Hint: Make a number line for (x + 3) and for (x - 2). Make three regions I, II and III. )

a -3 < x < 2

b x < 2 or x > 3

c x < -3 or x > 2

d 2 < x < 3

e nota

9.1

24.
What formula does this graph best represent?

a y =(9.9)^x

b y = (0.99)^x

c y = (1.05)^-x

d y = 6^-x

e nota

25.
What formula does this graph best represent?

a y = (1.6)^-x

b y = (1.4)^x

c y = 7^x

d y = (1.3)^x

e nota

9.2

26. f(x) = 4x - 3 and g(x) = 5x² + 5. Find f((g(x))

a 20x² + 5.

b 20x² + 3.

c 20x² + 11.

d 20x² + 17.

e nota

27. Find the inverse of f(x) = 5x + 9 (Hint: Let f(x) = y. Interchange y and x. Solve for y. )

a 5x + 9

b (x - 9)/5

c (x + 9)/5

d nota

9.3

28. log₅125 = w . Write in exponential form , and find w. (Hint : Draw an arrow between the base 5 and the w. This should remind you how to write the expression in exponential form.)

a 5^w = 125 and w = 5

b 5^w = 125 and w = 4

c w¹²⁵ = 5 and w = 1

d 5^w = 125 and w = 3

e nota

29. Write in logarithmic form. b⁴ = 81

a log_b3 = 81 and b = 9

b log81 = 3 and b = 3

c log_b81 = 5 and b = 3

d log_b81 = 4 and b = 3

e nota

30. Evaluate x without a calculator log₂8 = x. (Hint : Draw an arrow between the base 2 and the x to remind yourself how to write the expression in exponential form. Then solve for x. )

a 9

b 1

c 3

d nota

31. Evaluate x. log₁₀₀100⁹ = x. (Hint: See previous hint. Draw an arrow between the base 100 and x. Write in exponential form and solve for x. )

a 1/9

b 81

c 9

d nota

32. Evaluate and solve for x. ln e^10x = 30 (Hint: ln = log_e thus, log_ee^10x = 30. Draw an arrow between the base e and 30. Write in exponential form and solve for x.)

a x = 2

b x = 1

c x = 0

d x = 3

e nota

33. Evaluate and solve for x. log₁₀10^12x= 36 . (See previous hint.)

a x = 1

b x = 2

c x = 3

d nota

9.4

34. Evaluate ln(81/e¹⁵²). (Hint: ln = log_e and log_ee¹⁵² = 152.)

a ln81 - 152

b 152 - ln81

c ln152 - 81

d 152 + ln81

e nota

35. Simplify. log(1,000,000/x²⁴). (Hint: log = log₁₀ and log₁₀(1,000,000) = log₁₀10⁶. )

a 6 - log(24x)

b 7 + 2logx

c 5logx

d 6 - 24logx

e nota

36. Simplify.

a log x - 5log y

b 5·log x - log y

c log x - (1/5) log y

d nota

37. Simplify. log₄8 + log₄2 (Hint: Write the sum as the log of a product.)

a 1

b 2

c 3

d nota

38. Simplify. log₃27 - log₃3 (Hint: Write the difference as the log of a quotient.)

a 1

b 2

c 3

d 4

e nota

39. Simplify. 10 ln(x + 9) - 5 lnx.

a ln [(x + 9)/x⁵]

b ln [10(x + 9)/x⁵]

c ln [(x + 9)¹⁰/x⁵]

d nota

9.5

40. Solve for x. 2^{(2x -2)}= 64. (Hint: Write 64 as 2 raised to a power.) The value of x is in the ranges below:

a (0,3)

b (3,6)

c (6,9)

d (9,12)

e nota

41. 4^x = 32 Solve for x. (Hint : Write 4 as 2 raised to a power. Write 32 as 2 raised to a power.) x is in the range:

a (0,2)

b (2,4)

c (4,6)

d nota

42. Solve for x . 9e^x = 900. (Hint : First divide both sides by 9. Note: ln = log_e. )

a x = log₉ 100

b x = log 100

c x = ln 110

d x = ln 100

e nota

43. Solve for x. log₃x = 5. (Hint: Write in exponential form. Solve for x.)

a x = 81

b x = 243

c x = 27

d nota

44. Solve for x. log₅(x - 1) = 2. (Hint: Write in exponential form. Solve for x.)

a x = 12

b x = 22

c x = 32

d x = 26

e nota

45. Rewrite the following in exponential form: log₆(x - 1) + log₆x = 1. (Hint: Write the sum as the log of a product.)

a ( x - 1) + x = 6

b ( x - 1)·x = 6

c ( x - 1)·x = 36

d ( x - 1)·x = 1

e nota

46. Solve for x in the previous problem. x is in the following ranges:

a (-10, 0) or ( 0, 2)

b (-5, 0) or (0,4)

c (0,5) or (5,10)

d nota

written problems

47. Solve for x: log₃(x - 5) + log₃(x + 3) = 2.
Hint: Rewrite as log₃(x - 5)·(x + 3) = 2. Then write in exponential form.

48. Solve for x. log(2x - 1) - logx = 2. Log means log base 10. Subtraction must be converted to log of the quotient. Once you do that, convert to exponential notation, then cross multiply.

10.1

49. Find the distance d between the points (-2,-1) and (1,3).

50. Find the midpoint between the points (-2,-1) and (1,3).

51. Find the center and radius of the circle given by the equation here.
(x - 1)² + (y - 2)² = 25.

52. Find the center and radius of the circle given by the equation here.

x² + y² + 6x + 2y + 6 = 0.

Hint:

# Rewrite the equation as x² + 6x + y² + 2y + 6 = 0.

#Then complete the square twice for the terms that are in brackets:

(x² + 6x ) + (y² + 2y ) + 6 = 0

# After completing the square twice, factor the terms in brackets, collect like terms, and isolate the numbers to the right hand side.

53. Sec. 8.4. Solve for x: x⁴ - 9x² + 20 = 0. (Hint: Let: u = x²)

54. A problem for you visual learners. Sketch the inverse of the function below. Label the intercepts of the inverse.

55. Solve by completing the square:
x² + 10x = 24.

56. Solve by completing the square:
x² - 12x = 28.

8.2

57. Solve using the quadratic formula. x² + 3x + 1 = 0

58. Solve using the quadratic formula. x² + 3x - 8 = 0

59. Compute the discriminant x² + 3x + 7 = 0. How many solutions are there? Are they real or imaginary?

60. What are the solutions in the previous problem? ( In other words, solve for x in the previous problem using the quadratic equation.)

Extra credit

61. Solve for x. log₂x = 5. (Hint: Write in exponential form. Solve for x.)

62. Solve for x. log₃x = 3. (Hint: Write in exponential form. Solve for x.)

63. Solve for x. log₃9 = x (Hint: Write in exponential form. Solve for x.)

64. Solve for x. log₂16 = x (Hint: Write in exponential form. Solve for x.)

65. Solve for x. 2^{(2x -4)} = 32 (Hint: Write 32 as 2 raised to a power.)

66. Simplify: 64^2/3

67. Simplify: 8^2/3

The following problems would not be Extra Credit. They would be required. They are from Appendix G.

68. Complete the in the table for the function y = 1/x:

x	y
1
2
3
-1
-2
-3
1/2
1/3
-1/2
-1/3

69. Plot the graph of the previous problem.

70. Complete the in the table for the function y = 2/x:

x	y
1
2
3
-1
-2
-3
1/2
1/3
-1/2
-1/3

71. Plot the graph of the previous problem.