To calculate the average rate of change over the interval $-1 \leq x \leq 1$, we can use the formula for the average rate of change, which is given by:

$\frac{f(b) - f(a)}{b - a}$

where $a$ and $b$ are the endpoints of the interval, and $f(a)$ and $f(b)$ are the corresponding function values at these points.

Looking at the graph:

1. For $x = -1$, the function value $f(-1)$ appears to be $-4$.
2. For $x = 1$, the function value $f(1)$ appears to be $4$.

Using these points: $\text{Average rate of change} = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4 - (-4)}{1 + 1} = \frac{4 + 4}{2} = \frac{8}{2} = 4$

Thus, the average rate of change over the interval $[-1, 1]$ is $4$.

Would you like further explanation on this? Here are some related questions:

1. How does the average rate of change relate to the slope of a line?
2. What does it mean if the average rate of change is zero?
3. How do you interpret a negative average rate of change?
4. Can you find the average rate of change over a different interval?
5. How would the calculation change if the points were not on a straight line?

Tip: For linear functions, the average rate of change over any interval is the same and equals the slope of the line.