Worksheet: Rates of Change from Data

In this worksheet, we will practice calculating the rate of change and the average rate of change from data presented in a table.

Q1:

The table lists the distance covered in kilometers over a 15-hour hike. During which periods was the average speed below 2 kilometres per hour?

Hour 3 5 9 15
Distance 18 24 28 30
  • A between hour 5 and hour 15
  • Bbetween hour 3 and hour 5

Q2:

Let 𝑓 ( 𝑥 ) = 2 ( 3 𝑥 ) ( 𝑥 + 1 ) and 𝑔 be the quadratic function given by the following table.

𝑥 −2 −1 0 1 2 3
𝑔 ( 𝑥 ) 0 3 0 −9 −24 −45

Which of the following statements is true?

  • ABoth functions have the same axis of symmetry.
  • BThe minimum value of 𝑓 is greater than the maximum value of 𝑔 .
  • CThe sums of zeros of the two functions are the same.
  • DOn the interval 0 𝑥 3 , function 𝑓 has the higher average rate of change.
  • EOn the interval 0 < 𝑥 < 3 , function 𝑓 has the lower average rate of change.

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