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Use the image to answer the question.

A coordinate plane for f of x versus x.

Describe the graph of f(x)
by selecting the correct statement.

(1 point)
Responses

The average rate of change is negative on the interval [0,1]
and on the interval [3,4]
.
The average rate of change is negative on the interval left bracket 0 comma 1 right bracket and on the interval left bracket 3 comma 4 right bracket .

The average rate of change is negative only on the interval [1,3]
.
The average rate of change is negative only on the interval left bracket 1 comma 3 right bracket .

The average rate of change is negative on the interval [1,3]
and also on the interval [6,7]
.
The average rate of change is negative on the interval left bracket 1 comma 3 right bracket and also on the interval left bracket 6 comma 7 right bracket .

The average rate of change is negative only on the interval [6,7]
.

1 answer

To describe the graph of \( f(x) \) based on the average rate of change over the specified intervals, you would need to analyze the slope of the graph within those intervals.

  1. If the graph of \( f(x) \) is decreasing between two points, the average rate of change is negative on that interval.
  2. If the graph is increasing, the average rate of change is positive.

Since I can't view the image directly, I'll guide you through how to select the correct statement based on your analysis:

  • Check the intervals [0,1], [1,3], [3,4], and [6,7].
  • For each interval, look at the behavior of the graph:
    • If the graph is going down (decreasing), the average rate of change is negative.
    • If it's going up (increasing), the average rate is positive.

After analyzing the graph based on the intervals provided, select the statement that accurately reflects where the average rate of change is negative.

For example, if you find that the graph is decreasing in the intervals [0,1] and [3,4], select the first option. If it's only decreasing on [1,3] or only on [6,7], select the respective statements about those intervals.

Please provide the visual characteristics of the graph for a precise recommendation, or analyze it as described above to choose the correct statement.