To accurately select the correct statement regarding the average rate of change of the function \( f(x) \) on the specified intervals, we would need to analyze the graph of the function and determine the behavior of \( f(x) \) over those intervals.
If the graph is decreasing in the specified intervals, then the average rate of change would be negative for those intervals. Conversely, if the graph is increasing, the average rate of change would be positive.
Given the options presented:
- 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 only on the interval [1,3].
- 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 only on the interval [6,7].
Without access to the graph, I cannot definitively select the correct statement. However, you should look for the following:
- Check if the function \( f(x) \) is decreasing between 0 to 1 and 3 to 4 to support the first option.
- Examine the behavior between 1 to 3 to evaluate the second option.
- Look at the interval from 6 to 7 to confirm the third option.
- Finally, assess whether the function is only decreasing in the interval from 6 to 7 to consider the last option.
Once you determine how the function behaves over the specified intervals, you can choose the statement that accurately reflects the average rate of change for the function over those intervals.