Worksheet: Estimating Rates of Change and Areas Under Graphs

In this worksheet, we will practice estimating rates of change for points on a graph and estimating specified areas under graphs.

Q1:

The graph of a function 𝑔(π‘₯) is shown. Find the average rate of change over the interval of 1≀π‘₯≀4.

  • Aβˆ’3
  • B35
  • C13
  • Dβˆ’13
  • E3

Q2:

The graph of a function 𝑓 is shown. Estimate the rate of change for the function 𝑓 on the interval [βˆ’2,βˆ’1.5].

Q3:

The graph of a function 𝑓 is shown. The average rate of change of 𝑓 over the interval (0,π‘Ž) is βˆ’45. Which of the following comes closest to being a possible value of π‘Ž?

  • A5
  • B3
  • C1
  • D4
  • E2

Q4:

The graph of a function 𝑓 is shown, which is defined and continuous on (βˆ’βˆž,∞). The average rate of change of 𝑓 on the interval [1,5] is 3. Estimate 𝑓(5).

Q5:

The graph of a function is given below. Find the average rate of change of the function between the two points shown.

  • Aβˆ’117
  • B35
  • C711
  • D53
  • Eβˆ’35

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