To solve this question, we need to calculate the average rate of change of the function $f(x)$ over the interval $x = -2$ to $x = 0$. The average rate of change formula is:

$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a},$ where $a = -2$ and $b = 0$.

Step 1: Identify $f(-2)$ and $f(0)$

From the graph:

• At $x = -2$, the value of $f(x) = 9$.
• At $x = 0$, the value of $f(x) = 1$.

Step 2: Apply the formula

$\text{Average rate of change} = \frac{f(0) - f(-2)}{0 - (-2)} = \frac{1 - 9}{2} = \frac{-8}{2} = -4.$

Final Answer:

The average rate of change is -4.

Would you like a step-by-step explanation of how this formula works?

Related Questions:

1. What does the average rate of change represent geometrically on a graph?
2. How is the average rate of change different from the instantaneous rate of change?
3. What are the steps for identifying $f(a)$ and $f(b)$ from a graph?
4. How would the average rate of change be calculated for a different interval?
5. Can the average rate of change ever be zero, and if so, under what conditions?

Tip:

To avoid errors, always double-check the coordinates of the points you're using from the graph.