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Question

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 [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 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 only on the interval [6,7]
.
The average rate of change is negative only on the interval left bracket six comma seven right bracket .
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1 answer

To evaluate the average rate of change of the function \( f(x) \) over the specified intervals, we typically look at the slope of the secant line connecting the endpoints of each interval. If the value of \( f(x) \) decreases as \( x \) increases within that interval, the average rate of change is negative.

Since I cannot see the actual graph, I can provide guidance based on the information you're given:

  • For the intervals [0,1], [1,3], [3,4], and [6,7]:
    • If the function is decreasing (i.e., \( f(1) < f(0) \) for [0,1], \( f(3) < f(1) \) for [1,3], and so on), then the average rate of change is negative for those intervals.
    • Conversely, if the function is increasing over any of those intervals (i.e., \( f(1) > f(0) \) or \( f(3) > f(1) \)), then the average rate of change would be positive for those intervals.

Based on your choices, carefully analyze the graph to determine where the function decreases, and choose the statement that accurately reflects the intervals where the average rate of change is negative.

If you can recall specific behavior of the graph for those intervals, please apply that understanding to select your answer.