To estimate the average rate of change of the function shown in the graph from $x = 4$ to $x = 7$, we use the formula for the average rate of change:

$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

where $f(a)$ and $f(b)$ are the values of the function at $x = a$ and $x = b$, respectively.

Step 1: Estimate $f(4)$ and $f(7)$

From the graph:

• At $x = 4$, $f(4) \approx 7$.
• At $x = 7$, $f(7) \approx 6$.

Step 2: Plug into the formula

$\text{Average Rate of Change} = \frac{f(7) - f(4)}{7 - 4} = \frac{6 - 7}{3} = \frac{-1}{3} \approx -0.33$

Final Answer:

The estimated average rate of change from $x = 4$ to ( x = 7