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 [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 .
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].
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 [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 .
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].
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the graph of \( f(x) \), you need to look at the sections of the graph where the function decreases. The average rate of change on an interval \([a, b]\) can be determined by finding the change in the function values:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
If \( f(b) < f(a) \), the average rate of change is negative.
Based on typical interpretations of a graph:
1. Check the interval \([1, 3]\): If the graph is going downward between \( x = 1 \) and \( x = 3\), then the average rate of change is negative in this interval.
2. Check the interval \([6, 7]\): Similarly, see if the graph is descending between these points.
3. Look at the intervals \([0, 1]\) and \([3, 4]\) for any downward trends.
After evaluating these intervals based on the graph, you would select the appropriate statement.
If the average rate of change is negative for both \([1,3]\) and \([6,7]\), then the correct response would be:
"The average rate of change is negative on the interval \([1, 3]\) and also on the interval \([6, 7]\)."
If it's negative only in one of those intervals, pick the corresponding statement. Finally, if there's negativity in intervals like \([0,1]\) and \([3,4]\), you would choose that response instead.
Without seeing the specific graph, I cannot definitively choose which statement to select. Please analyze the graph according to these guidelines to identify the correct statement.
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
If \( f(b) < f(a) \), the average rate of change is negative.
Based on typical interpretations of a graph:
1. Check the interval \([1, 3]\): If the graph is going downward between \( x = 1 \) and \( x = 3\), then the average rate of change is negative in this interval.
2. Check the interval \([6, 7]\): Similarly, see if the graph is descending between these points.
3. Look at the intervals \([0, 1]\) and \([3, 4]\) for any downward trends.
After evaluating these intervals based on the graph, you would select the appropriate statement.
If the average rate of change is negative for both \([1,3]\) and \([6,7]\), then the correct response would be:
"The average rate of change is negative on the interval \([1, 3]\) and also on the interval \([6, 7]\)."
If it's negative only in one of those intervals, pick the corresponding statement. Finally, if there's negativity in intervals like \([0,1]\) and \([3,4]\), you would choose that response instead.
Without seeing the specific graph, I cannot definitively choose which statement to select. Please analyze the graph according to these guidelines to identify the correct statement.
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