To find the average rate of change of a function \( f(x) \) over the interval \([1, 4]\), we need to determine the values of \( f(1) \) and \( f(4) \). The formula for the average rate of change is given by:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 1 \) and \( b = 4 \).
Since I don’t have the actual image of the graph you referenced, I'll guide you on how to calculate it based on the provided information about the graph:
- Identify the value of \( f(1) \) and \( f(4) \) from the graph.
- Apply these values into the formula.
For example, if from the graph, we find:
- \( f(1) = 2 \) (as an arbitrary value)
- \( f(4) = 3 \) (as another arbitrary value)
We would calculate it as follows:
\[ \text{Average Rate of Change} = \frac{f(4) - f(1)}{4 - 1} = \frac{3 - 2}{3} = \frac{1}{3} \]
Assuming your graph depicts values differently, replace \( f(1) \) and \( f(4) \) with the actual values from your graph to derive the correct average rate of change.
Once you find the average rate of change using your graph, match your answer with the provided responses.