Example 3

Find the average rate of change of the function over the restricted intervals [–2, –1] and [–1, 1]. Determine if the rate of change over both intervals is positive, negative, 0, undefined, and/or constant. Use the graph of to explain how the average rate of change relates to the behavior of the graph across its whole domain.
  1. Calculate the average rate of change of over the interval [–2, –1].
  2. Calculate the average rate of change of over the interval [–1, 1].
  3. Determine if the rate of change over both intervals is positive, negative, 0, undefined, and/or constant.
  4. Graph .
  5. Describe what happens to the function values over the restricted domains [–2, –1] and [–1, 1].
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