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Praxis Middle School Mathematics: Functions

Inputs, outputs, graphs, and rates for middle school, including what to say when a student misreads a function.

Teacher certification exams are administered by testing organizations. FreeExam is not affiliated with those organizations, and these questions are original practice, not an official test.

Praxis is a trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.The rule is f(x) = 2x + 1. What is f(4)?

  2. 2.Which table shows a function?

  3. 3.A student says y = x² is not a function because the output 4 comes from both 2 and −2. What should the teacher say?

  4. 4.A graph fails the vertical line test. What does that tell the class?

  5. 5.A plant is 5 centimeters tall and grows 3 centimeters each week. Which rule gives the height after x weeks?

  6. 6.Using y = −2x + 8, what is y when x = 3?

  7. 7.A table shows (0, 4), (1, 7), and (2, 10). What is the rate of change?

  8. 8.Which equation matches a rate of 4 and a value of 1 when x = 0?

  9. 9.y = 6x gives the cost in dollars of x notebooks. What does the 6 mean?

  10. 10.A student graphs y = 2x + 3 by plotting (0, 2). What should the teacher point out?

  11. 11.For y = −x + 6, what is y when x = 6?

  12. 12.Two rules are y = 2x and y = 2x + 5. How do their graphs compare?

  13. 13.A student computes the rate between (1, 3) and (4, 9) as (1 − 4)/(3 − 9). What is the rate, and what was reversed?

  14. 14.Which situation is not a function?

  15. 15.y = (1/2)x. What is y when x = 8?

  16. 16.A rule is y = 5x. Which point is on its graph?

  17. 17.A class compares y = x + 2 and y = 3x. At x = 1, which output is larger?

  18. 18.The inputs 0, 1, 2, and 3 have outputs 0, 2, 8, and 18. A student says the rate is 2 because the second output is 2. What is a better description?

  19. 19.f(x) = x − 4. What is f(4)?

  20. 20.A taxi charges $3 plus $2 per mile. Which rule gives the charge for m miles?

  21. 21.A graph of distance versus time is a horizontal segment. What is the walker doing?

  22. 22.Which ordered pair fits y = −3x + 1?

  23. 23.A student fills a function table for y = x + 4 by adding 4 to the output to get the next output. The inputs are 1, 2, and 3. What should the outputs be?

  24. 24.The points (0, 0), (2, 6), and (4, 12) are on a graph. Which equation fits?

  25. 25.g(x) = 10 − x. What is g(3)?

  26. 26.A recipe uses 2 cups of oats for every 3 cups of flour. Which equation relates oats a to flour f?

  27. 27.A student says two different inputs cannot share an output. Which example should the teacher offer?

  28. 28.From x = 2 to x = 5, a function's output goes from 9 to 9. What is the rate of change on that interval?

  29. 29.h(x) = 4x. What is h(0)?

  30. 30.A savings account starts with $20 and then $5 is added each week. Which point is the amount after 3 weeks?

  31. 31.A graph rises from left to right, then falls. A student says it cannot be a function. When is the student wrong?

  32. 32.Which rule has the greater output at x = 4: y = 2x + 1 or y = x + 6?

  33. 33.p(n) = 8n gives the number of slices in n pizzas. What is p(3)?

  34. 34.A line passes through (0, −2) and rises 4 units for each 1 unit to the right. Which equation fits?

  35. 35.A student looks at y = 9 and says it is not a function because x does not appear. What is the right response?

  36. 36.The pairs are (1, 5), (2, 8), (3, 11), and (3, 14). Why is this not a function?

  37. 37.Using y = 2x − 5, what is y when x = 5?

  38. 38.Water in a tank is 12 liters and decreases by 2 liters each minute. Which rule gives the amount after t minutes, before the tank is empty?

  39. 39.A graph is described as a straight line through (0, 1) and (2, 5). A student says the rate is 1/2. What is the rate?

  40. 40.Which description matches a proportional relationship?

  41. 41.f(x) = x/4. What is f(12)?

  42. 42.A table for a function shows input 2 with output 11 and input 6 with output 11. What can the class conclude?

  43. 43.A distance graph falls as time increases. What does the fall mean?

  44. 44.y = −4x + 9. What is y when x = 2?

  45. 45.A rule is y = 7x + 2. Which input gives the output 23?

  46. 46.A student graphs y = x + 4 and y = x − 1 and says the lines will meet because both rates are 1. What should the teacher say?

  47. 47.For the rule 'output = input squared,' what is the output when the input is 6?

  48. 48.A function gives output 4 for input 1, output 7 for input 2, and output 10 for input 4. A student says the rate is 3 everywhere. What is wrong with that claim?

  49. 49.k(x) = 15 − 2x. What is k(4)?

  50. 50.Which equation says that y is 3 more than twice x?

  51. 51.A teacher asks for the output of y = 5x + 5 when x = 0. A student answers 5. Is that right?

  52. 52.The points (1, 2) and (3, 8) are on a straight-line graph. What is the rate of change?

  53. 53.A phone plan is $20 each month plus $3 for each gigabyte. What is the cost of 4 gigabytes in one month?

  54. 54.A student builds a table for y = 3x by listing outputs 3, 6, 9, 12 for inputs 0, 1, 2, 3. Which row is wrong?

  55. 55.Which pair is on the graph of y = x − 7?

  56. 56.A graph of a function is a vertical line. What is the teacher's correction of that description?

  57. 57.Compare y = 4x and y = 4x + 1 at x = 2. How do the outputs differ?

  58. 58.A function machine multiplies by 2 and then adds 1. Input 5 comes out as 11. A student says the machine added 6. What check shows the student's rule is different?

  59. 59.r(t) = 60t gives the distance in miles after t hours at a steady speed. What is r(2)?

  60. 60.Which table could be y = x + 8?

  61. 61.A line falls 2 units for each 1 unit it moves right, and it passes through (0, 5). Which equation fits?

  62. 62.Why is the set of points (2, 5), (2, 8), and (4, 5) not the graph of a function?

  63. 63.m(x) = 3x + 3. What is m(2)?

  64. 64.A candle is 20 centimeters tall and burns 3 centimeters each hour. Which expression is the height after h hours, while the candle remains?

  65. 65.s(n) = n² − 1. What is s(3)?

  66. 66.A graph through the origin has a constant rate of 5. Which equation fits?

  67. 67.A student says the rate between (0, 4) and (2, 4) is 4. What is the rate?

  68. 68.Which situation matches y = 8x?

  69. 69.f(x) = 6 − x. What is f(9)?

  70. 70.A line through (0, 6) has rate −1. Which point is also on the line?

  71. 71.A class is told that y = x² and y = 2x meet at x = 2. What are both outputs there?

  72. 72.Which change turns y = 3x + 1 into a proportional relationship?

  73. 73.Using the rule y = 9x − 4, what is y when x = 1?

  74. 74.A student reads the rate from (3, 1) to (5, 11) as (3 − 5)/(1 − 11) = 1/5. What is the rate?

  75. 75.A graph is a straight line that is not horizontal or vertical. What is true of its rate?

  76. 76.The input-output pairs (0, 2), (1, 5), (2, 8) follow which equation?

  77. 77.A pool has 40 liters and a hose adds 6 liters each minute. How much is in the pool after 5 minutes?

  78. 78.Why might a teacher ask for a second input after a student checks y = 2x + 6 against the simpler rule y = x + 8?

  79. 79.c(n) = 25n is the cost in cents of n stickers. What is c(4)?

  80. 80.A function's outputs for inputs 1, 2, 3, and 4 are 1, 4, 9, and 16. Which description fits?

  81. 81.y = 12/x is used only for nonzero x. What is y when x = 3?

  82. 82.Which pair of rules has the same rate?

  83. 83.A bicyclist is 2 miles from home and rides away at 10 miles per hour. How far from home is the rider after 3 hours at that speed?

  84. 84.A student claims every function graph must pass through (0, 0). Which counterexample should the teacher sketch?

  85. 85.t(n) = 4n + 4. What is t(0)?

  86. 86.The outputs of a function decrease by 5 each time the input increases by 1. The output at input 0 is 20. What is the output at input 3?

  87. 87.A map scale says 1 centimeter represents 5 kilometers. Which equation gives kilometers k from centimeters c?

  88. 88.Which of these inputs makes y = 2x + 8 and y = 4x equal?

  89. 89.w(x) = 100 − 20x. What is w(3)?

  90. 90.A teacher shows (1, 6), (2, 7), and (4, 9). A student says this must be y = 6x. Which row breaks that guess?

  91. 91.A temperature starts at 8 degrees and drops 2 degrees each hour. What is the temperature after 6 hours?

  92. 92.Which graph description is a function with rate 0?

  93. 93.q(x) = x/2 + 3. What is q(6)?

  94. 94.Two functions have rates 2 and 5. Both have output 0 when the input is 0. For a positive input, which has the greater output?

  95. 95.A printer charges $2 plus $0.10 for each page. What is the cost of 20 pages?

  96. 96.A student evaluates y = 5(x − 2) at x = 2 and gets 5. What is the output, and what step was skipped?

  97. 97.Which input gives y = 4x − 1 the output 15?

  98. 98.A distance graph is steep, then less steep, while staying increasing. What is happening to the speed?

  99. 99.v(n) = n + n. What is v(7)?

  100. 100.A function contains (2, 9) and (2, 1). A student wants to average 9 and 1 to repair it. What is the real issue?

  101. 101.y = −5x + 20. What is y when x = 4?

  102. 102.Which equation fits the pairs (0, −3), (1, 1), and (2, 5)?

  103. 103.A snack costs $1.50. There is no other fee. Which statement is true?

  104. 104.A student finds f(3) for f(x) = 2x + 4 by doing 2 × 3 × 4 = 24. What should the teacher have the student compute instead?

  105. 105.The rule is y = x + 10. What is y when x = 10?

  106. 106.A line has rate 1/2 and passes through (0, 3). What is the output when x = 4?

  107. 107.Which of these is a function of the input x?

  108. 108.A jar starts with 30 marbles, and 4 marbles are removed each turn. After how many turns are 6 marbles left?