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Accuplacer Rates of Change — practice questions

Explore 2 free Rates of Change questions in Accuplacer Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Rates of Change questions and exercises with answers

Showing questions 1–2 of 2.

What does the average rate of change of a function measure?Read the answer and worked solution →Find the average rate of change of f(x) = x squared + 3x on the interval from 1 to 5.Read the answer and worked solution →

Worked practice questions

What does the average rate of change of a function measure?

  1. Output change over input change
  2. Input change over output change
  3. Total output over total input
  4. Total input over total output
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Correct answer: A. Output change over input change

1. A rate of change compares how the output moves against how the input moves. 2. The average rate of change divides the change in output by the change in input. 3. Its units are always output units per input unit, such as dollars per year. 4. A falling output gives a negative average rate of change. _Source: OpenStax College Algebra (CC BY 4.0), section 3.3 Rates of Change and Behavior of Graphs_

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Find the average rate of change of f(x) = x squared + 3x on the interval from 1 to 5.

  1. It equals 36
  2. It equals 4
  3. It equals 11
  4. It equals 9
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Correct answer: D. It equals 9

1. Work out the output at each end of the interval first. 2. At x equal to 5, the square is 25 and 3 times 5 is 15, so the output is 40. 3. At x equal to 1, the square is 1 and 3 times 1 is 3, so the output is 4. 4. The change in output is 40 minus 4, which is 36. 5. The change in input is 5 minus 1, which is 4. 6. Dividing gives 36 over 4, which is 9. 7. The answer 36 stops at the change in output and never divides. 8. The answer 4 reports the change in input instead of the ratio. 9. The answer 11 averages the two outputs rather than comparing their change. _Source: OpenStax College Algebra (CC BY 4.0), section 3.3 Rates of Change and Behavior of Graphs_

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More Mathematics topics

Linear Equations in One VariableCoordinate Plane and GraphsLinear and Absolute Value InequalitiesRadical and Absolute Value EquationsComposition of FunctionsDomain and RangeFunctions and Function NotationInverse Functions