To determine which statement correctly describes the graph of \( f(x) \) based on the average rate of change, we need to understand what average rate of change means. The average rate of change of a function \( f \) between two points \( a \) and \( b \) is given by the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
A negative average rate of change indicates that the function is decreasing over the specified interval.
Without the specific graph of \( f(x) \), I can't provide an exact answer. However, you can analyze the graph of \( f(x) \) to determine where it is decreasing:
- Check the function values at the endpoints of each interval mentioned in the statements: \( [0, 1] \), \( [1, 3] \), \( [3, 4] \), and \( [6, 7] \).
- Calculate the average rate of change for each respective interval.
- Determine if the average rate of change is negative for each interval.
Once you perform this analysis, you can select the statement that accurately reflects the intervals where the average rate of change is negative. If you provide the graph or data of \( f(x) \), I can help clarify which statement is correct.