Average Rate of Change Quick Check

Question

3 of 53 of 5 Items

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

To determine the correct statement about the average rate of change of the function \( f(x) \) based on the provided intervals, we need to analyze the graph of \( f(x) \) on the specified intervals. Here’s how you might approach each option based on the expected behavior of the graph:

1. Average rate of change is negative only on the interval [6,7].
2. Average rate of change is negative on the interval [1,3] and also on the interval [6,7].
3. Average rate of change is negative only on the interval [1,3].
4. Average rate of change is negative on the interval [0,1] and on the interval [3,4].

To analyze:

• If the function is decreasing (moving downward as you move from left to right) in any of the specified intervals, the average rate of change will be negative.
• If it is increasing (moving upward), the average rate of change will be positive.

Since I cannot see the graph, you will need to identify which intervals produce a negative slope based on the behavior of the graph.

If the graph shows that:

• The function decreases from \( x = 1 \) to \( x = 3 \) and also from \( x = 6 \) to \( x = 7 \), then option 2 would be correct.
• If the function is decreasing only from \( x = 1 \) to \( x = 3 \), choose option 3.
• If it is decreasing from \( x = 0 \) to \( x = 1 \) and from \( x = 3 \) to \( x = 4 \), choose option 4.
• If it only decreases from \( x = 6 \) to \( x = 7 \), choose option 1.

Based on this analysis, you can select the correct statement that matches the observed behavior in the graph.