To calculate the average rate of change from $x = 4$ to $x = 7$, we use the formula:

$\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

Here, $x_1 = 4$ and $x_2 = 7$. From the graph:

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

Substitute the values:

$\text{Average Rate of Change} = \frac{f(7) - f(4)}{7 - 4} = \frac{6 - 7}{3} = \frac{-1}{3} = -0.333$

The estimated average rate of change from $x = 4$ to $x = 7$ is approximately -0.333.

Would you like me to explain further or perform additional calculations?

Here are 5 related questions to expand on this concept:

1. What is the significance of a negative average rate of change in this context?
2. How does the average rate of change differ from the instantaneous rate of change?
3. Can you estimate the instantaneous rate of change at $x = 5$ from the graph?
4. How would the average rate of change differ if the interval was $x = 4$ to $x = 6$?
5. What would the average rate of change be if the graph were linear?

Tip: The average rate of change provides insight into the overall trend of a function over an interval, even if the graph is not linear.