Accelerated Algebra I Final Review Linear and Exponential Functions 1. If f (x) = 3x 5 and the domain of f is {2, 4, 6}, what is the range of f (x)?

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1 Accelerated Algebra I Final Review Linear and Exponential Functions 1. If f (x) = 3x 5 and the domain of f is {2, 4, 6}, what is the range of f (x)? 2. Given the graph of f (x) below, what is f (2)? 3. If a n = a n and a 5 =12, what is a 7? 4. What is the rate of change for the function f(x) = 5(2) x 4 over the interval [8, 12]? 5. Given the equation and table below, compare the average rate of change and the y-intercept functions f(x) and g(x) 6. What is the y-intercept of the graph below?

2 7. Which explicit equation represents the pattern in the table below? 8. If f(x) = 5 x and g(x) = 6, what is (f g)(x)? 9. The recursive formula for an arithmetic sequence is given as a n = a n-1 + 9, with a 1 = 3. What is the seventh term of the sequence? 10. The explicit formula for a geometric sequence is an =3(-2) n-1. What is the fifth term of the sequence? 11. Given the graph of f (x) and g(x) below, which is the function rule for g(x) in terms of f (x)? 12. Leroy makes $9 per hour cleaning cars. His boss offers to pay him an additional $45 a week for cleaning the garage after work. What are the parameters in this scenario? 13. Describe the end behavior of y = 2 x. 14. If f(x) = 2x + 5, what is f(x + 1)? 15. Which of the following is an acceptable domain for a sequence? { 2, 1, 0, 1, 2, 3} 1 n 100 {1, 1.5, 2, 2.5, 3, 3.5} {2, 3, 4, 5,, } 16. An online company charges $5 a month plus $2 for each movie you decide to download. Graph this scenario. 17. If f(x) = 3x + 2 and g(x) = 7x 1, what is (f + g)(x)?

3 18. The fourth term in an arithmetic sequence is 7. If the sequence has a common difference of 3, what is the ninth term? 19. Jamal has a membership to a magazine club. He pays $5.00 per month for membership and $1.25 for each magazine he purchases. What are the parameters in this scenario? 20. Compare the functions f(x) and g(x), shown in the table and graph below Describing Data 21. Which data set is represented by the dot plot below? 22. What is the mean of the data set below? Which points in the data set below are outliers? What is the interquartile range of the data set below?

4 25. Ms. Rosenberg collects information about her students. She records students favorite movie type in the table below, and separates the responses by age. What is the joint frequency of 15-year-olds who prefer action movies? 26. What function is a good fit for the data in the scatter plot below? 27. A linear function is used to estimate a data set. The residuals of the line fitted to the data are determined and are included in the residual plot below. What does the residual plot tell you about the line fitted to the data?

5 28. What linear function is a good fit for the data in the scatter plot below? 29. A car manufacturer is interested in learning about the amount of money people of different ages spend on a new car. Data regarding customer age and car purchase price are listed in the table below. What is the correlation between age and car price? 30. The events x and y have a correlation coefficient of r = What is the relationship between x and y? 31. Nolan uses the equation y = 7.5x to estimate the time it will take him to run between 1 and 5 miles, where x is the number of miles and y is the time in minutes. Which statement is true based on the equation? 32. What linear function is a good fit for the data in the table below?

6 33. What is the median of the data set used to create the box plot below? 34. What is the interquartile range of the data below? Look at the data presented in the histograms below. What comparison is true? 36. Ruby asks her classmates how many hours they sleep each night during the week, and separates the responses by gender in the two-way frequency table below. What is the joint frequency of males who sleep 8 10 hours? 37. Anna asks her friends which book they prefer in a trilogy. She separates the responses by age. What is the marginal frequency of Book 1?

7 38. Sam tracks the growth of a plant, and records its height in centimeters each week. He determines that the equation y = 2.3x + 16 can be used to estimate the plant s height for any week. What statement is true based on Sam s equation? 39. A data set has a correlation coefficient of What statement about the data set is true? 40. Isabella makes deposits to her savings account each month, and she also earns interest. She records the amount of money in her savings account each month, and finds that the equation y = 218x can be used to estimate the dollars in her savings account for any month. What statement is true based on Isabella s equation? Transformations in the Coordinate Plane 41. The mathematical statement AB CD means: 42. Given the diagram below, what is a true statement? 43. What type of transformation moves P (3, 7) onto P (3, 7)? 44. The point A ( 5, 2) has undergone the transformation T 1, 2. What point is the preimage of A? 45. Which shape below has one line of symmetry?

8 46. What relationship is formed by a line of symmetry and the line segment between opposite points in the symmetry? 47. If f (x, y) ( y, x) and g(x, y) (6, 3), then what is f ( g(x, y))? 48.Given the diagram below, state the image of ABC under R 90 (T 2, -1). 49. When a preimage point is transformed through a reflection over a given line, what statement describes the point s movement? 50. Given A ( 5, 7) and T(x + 3, y 8), state A" after a reflection over the x-axis of the point T(A). 51. Find R m such that R m (ΔABC ) is equivalent to r y = x (r y (ΔABC )).

9 52. In what quadrant is P" = T 1, 4(T 1, 4) given P ( 8, 5)? 53. What is the measure of a right angle? 54. What type of function maps an input onto itself? 55. How many lines of symmetry does a square have? 56. What geometric figure has an infinite number of lines of symmetry? 57. How many components does every point in the coordinate plane have? 58. What type of rotation does a rotation transformation require? 59. What type of reflection does a reflection transformation require? 60. Translation transformations move all points: Right Triangle Trigonometry Use the figure below to answer questions 61-63: 61. Given ΔABC, find the sine of A. 62. Given ΔABC, find the cosine of A. 63. Given ΔABC, find the tangent of B. 64. ΔABC is a right triangle. One of the acute angles measures 24º. What is the cosine of the other acute angle?

10 65. For what value of θ is cos θ = sin 82º? 66. Given ΔABC below, what are the measures of segment AC, A, and B? 67. A right triangle has one leg that measures 8 feet and another that measures 15 feet. What are the measures of the acute angles? 68. A 7-meter-tall ladder is placed against a wall. The ladder is on level ground at an angle of 78º to the ground. About how far up the wall does the top of the ladder reach? 69. ΔABC is equilateral. What are the cosecant, secant, and cotangent of A? 70. Given ΔABC below, what are the measures of A and B?

11 71. A monument is 75 meters high. At an information booth, an observer notices the angle of elevation to the top of the monument is 36º. How far is the observer from the base of the building? 72. An airplane is flying at a height of 7 miles above the ground. The distance along the ground to the airport is 15 miles. What is the angle of depression from the airplane to the airport? 73. If the sine of 30º = 0.5, what is the cosine of 60º? 74. Find a value of θ for which sin θ = cos 25º is true. 75. ΔABC is a right triangle. One of the acute angles is 38º. What is the cosine of the other acute angle? 76. Use your calculator to find the sine of 61º. 77. A 15-foot ladder is placed against a wall. The ladder is on level ground at an angle of 68.5º to the horizontal. About how far up the wall will the top of the ladder be located? 78. You sight a rock climber on a cliff at a 29º angle of elevation. Your eye level is 6 feet above the ground and you are 1,000 feet from the base of the cliff. What is the approximate height of the rock climber from the ground?

12 79. A skateboard ramp is 40 feet long and rises from the ground at an angle of 33º. What is the vertical rise of the ramp? Round to the nearest thousandth. 80. Solve the right triangle below. Round sides to the nearest thousandth and angles to the nearest degree.