ALGEBRA DOMAIN (approximately 36% of test) Which function is shown on the graph? a. y = x 2 b . y = x 3 c

1. ALGEBRA DOMAIN (approximately 36% of test) Which function is shown on the graph? a. y = x2 b. y = x3 c. y = | x | d. y = 1/x 2. Sam observes that the data he collected falls in a V-shaped pattern when he graphs it. What type of function would best represent Sam’s data? a. absolute value b. cubic c. inverse d. quadratic

2. 3. Which function is shown on the graph? a. y = x2 b. y = x3 c. y = | x | d. y = 1/x Anne observes that the data she collected falls in a parabola-shaped pattern when she graphs it. What type of function would best represent Anne’s data? a. absolute value b. cubic c. inverse d. quadratic

3. 5. The graph of f(x) = x2 is • transformed to produce the • graph shown at the right. • Which function would • produce this transformation? • g(x) = (x + 3)2 b. g(x) = (x – 3)2 • c. g(x) = x2 + 3 d. g(x) = x2 – 3 • 6. The graph of f(x) = | x | is • transformed to produce the • graph shown at the right. • Which function would • produce this transformation? • a. g(x) = | -x | b. g(x) = | 2x | • c. g(x) = - | x | d. g(x) = | 1/x |

4. 7. The graph of f(x) = x2 is • transformed to produce the • graph shown at the right. • Which function would • produce this transformation? • a. g(x) = 2x2 b. g(x) = 0.5x2 • c. g(x) = -x2 d. g(x) = (-x)2 • 8. A section of Bill’s graphic design for a client’s logo is • represented in his computer graphic program as a cubic • function, f(x) = x3. He needs to modify his design by copying • that part of the design 5 units to the left. Which function • should he use to create this transformation of his original • function? • g(x) = 5x3 b. g(x) = x8 • c. g(x) = (x – 5)3 d. g(x) = (x + 5)3

5. 11. For the function f(x) = x3, which statement below is true? • As x approaches ∞, f(x) approaches ∞, • and as x approaches -∞, f(x) approaches ∞. • As x approaches ∞, f(x) approaches ∞, • and as x approaches -∞, f(x) approaches -∞. • As x approaches ∞, f(x) approaches -∞, • and as x approaches -∞, f(x) approaches ∞. • As x approaches ∞, f(x) approaches -∞, • and as x approaches -∞, f(x) approaches -∞. • What are the zeros of function • shown on the graph at the right? • a. 2 and -3 • b. -2 and 3 • c. -6 • c. 0

6. What is the range of the • function in the graph • shown at the right? • a. ( -∞, ∞) b. ( 3, -2 ) • c. [ -2, ∞) d. [ 0, ∞) • What is the domain of the • function in the graph • shown at the right? • a. all real numbers except 0 • b. all real numbers except 1 • c. all real numbers • d. all integers

7. Colin is developing a catapult for a contest in which the participants compete to see which team’s pumpkin will stay in the air the longest and which will travel the longest distance. As he considers adjustments to his catapult, he uses computer simulations to track the distance the pumpkin travels as a function of time in the air for each test throw. Should Colin’s graphs show a continuous function, or discrete points? a. continuous b. discrete

8. Dexter monitors the mosquito population in a certain • region by counting the number of mosquitoes in a mosquito trap at the end of each day. During a particularly wet fourteen-day period, he notices that the mosquito population numbers are increasing in a quadratic pattern. If he wants to prepare a graph to show the population growth for that period, what would be an appropriate domain for his graph? • real numbers from -∞ to ∞ • b. real numbers from 0 to ∞ • integers from 1 to 14 • d. integers from 1 to ∞

9. Use the graph below for problems 15 and 16. Company Profit 15. According to the graph, during what year did the company earn its maximum profit? a. 2003 b. 2006 c. 2009 d. 2020 Profit (in millions of dollars) Years Since Business Opened in 2001

10. Between what years did the company see the largest • increase in profits? • a. between the first and second years of business • b. between the fifth and sixth years of business • c. between the sixth and seventh years of business • d. between the eighth and ninth years of business • What is an explicit formula for the sequence shown? • 4, 9, 14, 19, 24, . . . • a. an = 4n + 5 b. an = 4n + 9 • c. an = 5n + 4 d. an = 5n – 1

11. 18. Figure 1 Figure 2 Figure 3 Figure 4 If the pattern continues, which formula shows the number of squares that will be on the bottom row of the nth figure? a. an = n b. an = n + 2 c. an = 2n – 1 d. an = n2

12. Which of the following sequences is best defined by a • recursive rather than explicit formula? • a. 2, 5, 8, 11, 14, . . . b. 3, 6, 12, 24, 48, . . . • c. 32, 28, 24, 20, 16, . . . d. 0, 1, 1, 2, 3, 5, 8, 11, . . . • Which of the following could be the domain of the • sequence below? • 1, 7, 13, 19, 25 • a. real numbers from 1 to 5 • b. integers greater than 0 • c. integers from 1 to 5 • d. all real numbers

13. Use the following graph for problems 21 and 22. During which interval of hours is the rate of change constant? a. 1 to 3 hours b. 3 to 5 hours c. 5 to 7 hours d. 7 to 9 hours

14. What was the average rate of change in the number of • miles between the sixth and ninth hours? • a. approximately 1.7 miles per hour • b. approximately 3.5 miles per hour • c. approximately 1.2 miles per hour • d. approximately 6 miles per hour

15. 23. Which function has the greatest average rate of change between x = 0 and x = 3? a. y = 2x b. y = x2 c. y = .25x3 d. The rates of change are equal.

16. Which of the following would have a constant rate of change throughout the function? a. an absolute value function b. a cubic function c. a linear function d. a quadratic function Which of the following functions is symmetric with respect to the origin? a. y = x3 b. y = x2 c. y = | x | d. y =

17. 26. Which statement describes the function f(x) = x2 – 3? • a. The function is symmetric with respect to the origin. • b. The function is symmetric with respect to the y-axis. • c. The axis of symmetry for the function is y = -3. • d. The function has no symmetry. • Which statement describes the function shown on the • graph below? • a. The function is symmetric with respect to the origin. • b. The function is symmetric with respect to the y-axis. • c. The axis of symmetry for the function is x = 2. • d. The function has no symmetry.

18. 28. Which statement describes the function f(x) = 4x3? • a. The function is symmetric with respect to the origin. • b. The function is symmetric with respect to the y-axis. • c. The axis of symmetry for the function is y = -3. • The function has rotational symmetry about the point (0, 3). • 29. To solve the equation • x2= 2x, Evan graphed • f(x) = x2 and g(x) = 2x. • What are the solutions • for the equation? • a. 0 and 4 • b. all real numbers • c. all integers • d. 0 and 2

19. 30. To solve the equation ½ x + 1 = 2x + 7, Fred graphed f(x) = ½ x + 1 and g(x) = 2x + 7. What is the solution for the equation? a. 1 b. 7 c. -1 d. -4 31. To solve the equation x3= -x2 + 2, Greg graphed f(x) = x3 and g(x) = -x2 + 2. What is the solution for the equation? a. 2 b. 0 c. -1 d. 1

20. 32. The functions f(x) = x2 – 4x + 3 and g(x) = -x2 + 4x – 3 are graphed on the coordinate grid at the right. What is the value of x in the equation x2– 4x + 3 = -x2 + 4x – 3? a. 3 or -3 b. 1 or 3 c. 0 d. no solution 33. What is the inverse of the function f(x) = 5x2 + 8? a. f-1(x) = b. f-1(x) = c. f-1(x) = d. f-1(x) =

21. Given the function shown in the table below, what is the domain of the inverse of the function? X 1 3 5 7 Y 2 10 26 50 a. { 1, 3, 5, 7 } b. { -1, -3, -5, -7 } c. {2, 10, 26, 50 } d. {-2, -10, -26, -50 } The graph of f(x) has a restricted domain. Its inverse, f-1(x), and the dashed line y = x are also graphed . Which set of values indicates the restricted domain of f-1(x)? a. -5 < x < 8 b. -5 < x < 2 c. 1 < x < 8 d. 1 < x < 2

22. If f(x) = x3 and f-1(x) = , what is the value of f(f-1(8))? a. 2 b. 8 c. 16 d. 512 37. Write as a complex number in standard form. a. 3 b. -3 c. 3i d. -3i 38. Which is equivalent to ? a. 4 b. 4i c. d. 39. Which is equivalent to ? a. 9 b. 9i c. d. 40. Write as a complex number in standard form. a. 7 b. 2 + 5i c. 2 – 5i d. -3

23. 41. Add: (3 + 2i) + (-5 + 7i). a. -2 + 9i b. -16 c. -2 – 5i d. 14 42. Simplify: i25 a. -1 b. 1 c. –i d. i 43. Multiply: (3 – 4i)(2 + 5i) a. 26 b. 6 – 20i2 c. 5 + i d. 26 + 7i Simplify: a. b. c. d.

24. 45. Simplify: a. b. c. d. Simplify: a. 6a2b4b. 6ab2c. d. 47. Simplify: a. b. c. d. Simplify: a. b. c. d.

25. 49. Simplify: a. b. c. 39 d. 50. For which expression below should the denominator be rationalized? I. II. III. a. I only b. I and II c. II and III d. I and III 51. Simplify: a. b. c. 420 d. Which expression is equivalent to ? a. b. c. d.

26. 53. Add: (x2 + 7x + 5) + (2x – 9) a. x2 + 9x + 4 b. 10x2 – 4 c. 10x2 + 4 d. x2 + 9x – 4 54. Multiply: (x – 6)(x + 4) a. x2 – 2x – 24 b. x2 – 24 c. 2x – 24 d. x2 + 2x – 24 55. Multiply: (x – 6)(x2 – 2x + 5) a. x3 + 12x + 5 b. x3 – 8x2­ + 17x – 30 c. x3 – 2x2 – 30 d. –x2 – 30 56. Simplify: (2x2 – 3x + 4) + (3x2 – 6) – (x + 11) a. 5x2 – 4x – 13 b. 5x‑2 – 2x – 13 c. 5x2 – 9x – 7 d. 5x2 – 4x + 9

27. Simplify: a. b. c. d. Simplify: a. b. c. d.

28. Simplify: a. b. c. d. Simplify: a. b. c. d.

29. 61. Find the complete factorization of 2x5 – 6x3. a. 2x3(x2 – 4x) b. 2x5(1-3x2) c. -4x2 d. 2x3(x2 – 3) 62. Factor: 9x2 – 16 a. (9x-16)(x+1) b. (3x + 8)(3x – 8) c. (9x – 4)(x + 4) d. (3x – 4)(3x + 4) 63. Factor: 16x2 + 9 a. (4x + 3)(4x + 3) b. (4x + 3i)(4x – 3i) c. (8x + 3)(8x + 3) d. (8x + 3i)(8x – 3i) 64. Factor: 2x2 + 9x – 5 a. (2x + 1)(x – 5) b. (2x – 1)(x + 5) c. (2x – 5)(x + 1) d. (2x + 5)(x – 1)

30. Simplify: a. b. c. d. 66. Simplify: a. x2 b. c. d. 2x2 Simplify: a. b. c. d. 68. Simplify: a. 4 b. c. 2 d.

31. 69. Solve for x: a. 65 b. 63 c. 9 d. 7 70. Solve for x: a. 1 b. 121 c. 11 d. -1 Solve for x: a. b. c. -2 d. 4 72. Solve for x: a. 2 b. -2 c. 4 d. -10

32. 73. Solve for x: a. -1 b. 1 c. -2 d. 2 74. Solve for x: a. -2 or 10 b. -6 or 40 c. -10 or 4 d. no solution 75. Solve for x: a. -8 b. 4 c. 10 d. -3 Solve for x: a. -2 or 6 b. 2 or -6 c. -3 or -4 d. 3 or 4

33. 77. What is the range of the following function? • a. (-∞, ∞) b. all whole numbers • c. all integers d. [1, ∞) • 78. What is the vertex of y = 4 | x – 3 | – 6? • a. (-12, 6) b. (3, -6) c. (-3, -6) d. (3, 6) • 79. Over what interval is f(x) increasing? • a. (5, ∞) b. (-∞, 5) c. (-∞,∞) d. (0, ∞) • 80. Find the x-intercept and y-intercept of the function: • a. x-intercept = -2; y-intercept = 2 • b. x-intercept = -2; y-intercept = -2 • c. x-intercept = 2; y-intercept = -2 • d. x-intercept = 2; y-intercept = 2

34. Solve: | 2x + 3 | = 11 a. 4, 7 b. , c. 4, -7 d. -4, 7 Solve: | a + 5 | > 3 a. a < -8 or a > -2 b. -8 < a < -2 c. a < -3 or a > 3 d. -3 < a < 3

35. 83. According to the graph, for what value(s) of x does f(x) = 4? a. x = 3 or x = 0 b. x = -1 or x = 7 c. x = -4 or x = 4 d. x = 4 or x = 3 According to the graph, what is the solution for the inequality | x + 2 | > 3? a. x < -5 or x > 1 b. -3 < x < 3 c. -5 < x < 1 d. all real numbers

36. 85. Which is equivalent to (2x2)-3? a. b. c. d. 86. Simplify: (n3p4)8 a. n11p12 b. n24p32 c. (np)56 d. (np)96 Simplify: a. b. c. d. 88. For a planned mission, a spacecraft will travel 8.2 x 108 miles to Saturn. The craft will travel at a speed of 7.4 x 104 miles per hour. How many hours will it take the craft to reach Saturn? a. 1.1 x 1012 hours b. 6.1 x 1013 hours c. 1.1 x 104 hours d. 6.1 x 104 hours

37. 89. What is the y-intercept of the graph of the function y = 3(2)x? • a) (0, 1) b. (0, 2) c. (0, 6) d. (0, 3) • Which statement is true about the end behavior of the graph of f(x) = -3(0.5)x? • a. As x approaches infinity, f(x) approaches 0. • As x approaches –∞, f(x) approaches –∞. • As x approaches ∞, f(x) approaches ∞. • As x approaches –∞, f(x) approaches 0. • c. As x approaches ∞, f(x) approaches – ∞. • As x approaches – ∞, f(x) approaches 0. • d. As x approaches ∞, f(x) approaches 0. • As x approaches –∞, f(x) approaches ∞.

38. Which function has a graph that is increasing over the entire domain? a. f(x) = (0.25)x b. f(x) = -2(3)x c. f(x) = 3(2)x d. f(x) = 3x2

39. The declining • population of • wolves in a particular • region is modeled • by the exponential • function shown. • What does the x-intercept • represent in the context of the problem? • a. the number of wolves at the beginning of the study • b. the number of years after which there would be no • wolves left if the pattern continues • c. the maximum number of wolves during the period of • the study • d. the year 2005 Number of Wolves (hundreds) Number of Years Since Beginning of Study in 2005

40. 93. Which function does the graph represent? • a. f(x) = 2x • b. f(x) = 2-x • c. f(x) = -x2 • d. f(x) = -2x

41. Which table can be modeled by the equation y = 2(0.6)x? a. x -2 0 1 2 y 1/18 2 12 72 b. x -2 0 1 2 y -2.4 0 1.2 2.4 c. x -2 0 1 2 y 0.6 0.6 0.6 0.6 d. x -2 0 1 2 y 5.55… 2 1.2 0.72

42. Which function does • the graph represent? • a. f(x) = 2x + 3 • b. f(x) = 2x – 3 • c. f(x) = 2x-3 • d. f(x) = 2x+3 • Which function does • the graph represent? • a. f(x) = 2x + 3 • b. f(x) = 2x – 3 • c. f(x) = 2x-3 • d. f(x) = 2x+3

43. 97. Solve for x: 3x + 2 = 81 a. 25 b. 2 c. 27 d. -5 98. Use the graph of y = 3x – 5 to solve for x when y = -2. a. -5 b. -4 c. 1 d. 1.5

44. 99. Solve: 4x + 3 > 19 a. x > 2 b. x < 3 c. x > 0 d. x < -2 If there are initially 20 bacteria in a sample, and the number of bacteria is increasing by 50% every hour, the number of bacteria after t hours can be found using the formula N = 20(1.5)t. A model of the function is shown on the graph below. After approximately how many hours will the number of bacteria exceed 100? a. 2 b. 4 c. 6 d. 50

45. A geometric sequence follows the rule an = 100 · 5n-1. What is the domain of the sequence? a. all real numbers b. all positive numbers c. all integers d. all positive integers 102. What are the first five terms in the geometric sequence for which a1 = 3 and r = 5? a. 3, 8, 13, 18, 23 b. 3, 8, 11, 16, 19 c. 5, 15, 45, 135, 405 d. 3, 15, 75, 375, 1875

46. What are the first five terms in the geometric sequence defined by the rule an = 3n-1? a. 1, 3, 9, 27, 81 b. 3, 6, 9, 12, 15 c. 3, 2, 1, 0, -1 d. 3, 4, 5, 6, 7 In a particular geometric sequence, a1 = 7 and a2 = 14. Which answer shows a rule that could be used to find the nth term of that sequence? a. an = 7n b. an= 2 · 7n c. an = 7 · 2n – 1 d. an = 14n – 1

47. Which rule below could apply to a geometric sequence that has a common ratio of 6? a. an = 6 · 2n-1 b. an = 25 · 6n-1 c. an = 6n – 5 d. an = x6 Write a rule for the nth term of the geometric sequence. 3, 12, 48, 192, . . . a. an = 4 · 3n - 1 b. an = 4n – 1 c. an = 3 · 4n – 1 d. a­n = 192 · (0.25)n

48. 107. Due to a decreasing number of predators, the population of forest mice in a particular region is doubling every year. If the population of mice was estimated to be 1000 when data was first collected, how many mice would be expected to be in the population 6 years later? a. 64,000 b. 6,000 c. 12,000 d. 100,000 A certain antibiotic is found to reduce the number of germ cells by 75% of each time a dose is given. In a certain sample, if there are originally 2000 germ cells, approximately how many would remain after 4 doses of the antibiotic? a. 633 b. 8 c. 122 d. 15

49. Find the domain and range for y = log3(x – 2) a. domain: all real numbers; range: y > 2 b. domain: all real numbers; range: y > 0 c. domain: x > 0; range: all real numbers d. domain: x > 2; range: all real numbers 110. What is the y-intercept of y = 4 · 11n – 1? a. 4 b. 11 c. 44 d. 0 111. Which line is an asymptote for y = 3 + log x? a. x = 3 b. y = 0 c. y = 3 d. x = 0 112. Which function increases on the interval (-∞, ∞)? a. y = 0.25x b. y = -(2x) c. y = 4-x d. y = 3x

50. Change y = x2 – 6x + 8 into general (vertex) form. • a. y = (x – 3)2 – 1 b. y = (x – 3)2 + 8 • b. y = (x – 6)2 + 8 d. y = (x + 4)2 – 6 • 114. What are the x-intercepts and vertex of the quadratic • function y = x2 + 10x + 16? • a. x-intercepts: 10 and 16; vertex (0, 0) • b. x-intercepts: -8 and -2; vertex (-5, -9) • c. x-intercepts: -10 and -16; vertex (-13, -10) • d. x-intercepts: 8 and 2; vertex (5, -9)