To find the average rate of change of a function \( f(x) \) over the interval \([1, 4]\), we use the formula:
\[ \text{Average rate of change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 1 \) and \( b = 4 \). We need the values of the function at these points, \( f(1) \) and \( f(4) \).
Since I cannot see the image you mentioned, I advise you to determine \( f(1) \) and \( f(4) \) based on the graph. Once you have those values, substitute them into the formula to calculate the average rate of change.
For example, if you find that \( f(1) = 2 \) and \( f(4) = 5 \):
\[ \text{Average rate of change} = \frac{5 - 2}{4 - 1} = \frac{3}{3} = 1 \]
If you provide the values for \( f(1) \) and \( f(4) \) from the graph, I can help you calculate the average rate of change and match it to the responses listed.