To find the average rate of change of the function $f(x)$ over the interval $[-2, 2]$, we need to apply the formula for the average rate of change:

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

where $a = -2$ and $b = 2$.

1. Determine $f(-2)$: From the graph, when $x = -2$, the value of $f(x)$ appears to be $f(-2) = -2$.

2. Determine $f(2)$: Similarly, when $x = 2$, the value of $f(x)$ appears to be $f(2) = 2$.

3. Apply the values: $\text{Average Rate of Change} = \frac{f(2) - f(-2)}{2 - (-2)} = \frac{2 - (-2)}{2 + 2} = \frac{2 + 2}{4} = \frac{4}{4} = 1$

So, the average rate of change for $f(x)$ over the interval $[-2, 2]$ is $\frac{1}{1} = 1$.

Would you like more details, or do you have any questions?

Here are some related questions to explore further:

1. What does the average rate of change signify for a linear function?
2. How does the average rate of change differ for non-linear functions?
3. Can the average rate of change be negative, and what would that indicate about the function?
4. How do we interpret the slope of a linear function on a graph?
5. What is the relationship between average rate of change and the derivative of a function?

Tip: For a linear function, the average rate of change over any interval is equal to the slope of the line.