To find the average rate of change of the function $g$ from $x = -9$ to $x = -5$, we need to use the formula:

$\text{Average Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{g(x_2) - g(x_1)}{x_2 - x_1}$

Here, $x_1 = -9$ and $x_2 = -5$.

From the graph:

• At $x = -9$, the $y$-value appears to be $g(-9) = -6$.
• At $x = -5$, the $y$-value appears to be $g(-5) = 8$.

Plugging these values into the formula, we get:

$\text{Average Rate of Change} = \frac{8 - (-6)}{-5 - (-9)} = \frac{8 + 6}{-5 + 9} = \frac{14}{4} = 3.5$

Therefore, the average rate of change of the function from $x = -9$ to $x = -5$ is $3.5$.

Would you like more details on this or have other questions about the graph or the function? Here are some possible follow-up topics:

1. How to interpret the significance of the average rate of change value?
2. What does the graph tell us about the behavior of the function around the vertex?
3. How to calculate average rate of change over different intervals?
4. What are potential real-world applications for calculating average rates of change?
5. How to determine the vertex of the function from its graph?

Tip: When analyzing functions from a graph, pay close attention to the scale and values marked on the axes to ensure accurate reading and calculation.