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]
.
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]
.
Answers
Answered by
GPT-4o mini
To accurately select the correct statement regarding the average rate of change of the function \( f(x) \) over specific intervals, we need to analyze the behavior of the graph in each specified interval.
Here's a breakdown of the required analysis:
1. **Negative Average Rate of Change**: This occurs when the function \( f(x) \) decreases over the interval. If the graph slopes downward as you move from left to right over that interval, the average rate of change is negative.
2. **Intervals to Analyze**:
- [0,1]
- [1,3]
- [3,4]
- [6,7]
3. **Statements to Consider**:
- (1) Average rate of change negative only in [6,7].
- (2) Negative on [1,3] and [6,7].
- (3) Negative only in [1,3].
- (4) Negative on [0,1] and [3,4].
### Selection Process:
- If the graph shows a decrease (negative slope) over intervals [1,3] and [6,7], we would choose statement (2).
- If it shows a decrease only on [1,3], we would select statement (3).
- If the interval [6,7] is the only one where it decreases, then statement (1) would be correct.
- Similarly, if it decreases in the intervals [0,1] and [3,4], we would choose statement (4).
Without the diagram, I'd recommend checking the graph carefully based on the symptoms described above to determine which statement accurately reflects the patterns present in the graph of \( f(x) \).
Here's a breakdown of the required analysis:
1. **Negative Average Rate of Change**: This occurs when the function \( f(x) \) decreases over the interval. If the graph slopes downward as you move from left to right over that interval, the average rate of change is negative.
2. **Intervals to Analyze**:
- [0,1]
- [1,3]
- [3,4]
- [6,7]
3. **Statements to Consider**:
- (1) Average rate of change negative only in [6,7].
- (2) Negative on [1,3] and [6,7].
- (3) Negative only in [1,3].
- (4) Negative on [0,1] and [3,4].
### Selection Process:
- If the graph shows a decrease (negative slope) over intervals [1,3] and [6,7], we would choose statement (2).
- If it shows a decrease only on [1,3], we would select statement (3).
- If the interval [6,7] is the only one where it decreases, then statement (1) would be correct.
- Similarly, if it decreases in the intervals [0,1] and [3,4], we would choose statement (4).
Without the diagram, I'd recommend checking the graph carefully based on the symptoms described above to determine which statement accurately reflects the patterns present in the graph of \( f(x) \).