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Worksheet: Rates of Change from Data

Q1:

The table lists the distance covered in kilometers over a 15-hour hike. During which periods was the average speed below 2 kilometers 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 ( π‘₯ ) = 2 ( 3 βˆ’ π‘₯ ) ( π‘₯ + 1 ) and 𝑔 be the quadratic function given by the following table.

π‘₯ βˆ’2 βˆ’1 0 1 2 3
𝑔 ( π‘₯ ) 0 3 0 βˆ’9 βˆ’24 βˆ’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 ≀ π‘₯ ≀ 3 , function 𝑓 has the higher average rate of change.
  • EOn the interval 0 < π‘₯ < 3 , function 𝑓 has the lower average rate of change.