To find the average rate of change of the function $f(x)$ on the interval $-1 \leq x \leq 1$, we can use the formula for the average rate of change:

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

where $a = -1$ and $b = 1$. Now, we need to estimate the values of $f(x)$ at $x = -1$ and $x = 1$ by observing the graph.

From the graph:

• At $x = -1$, it looks like $f(-1) \approx -8$.
• At $x = 1$, it looks like $f(1) \approx -4$.

Now, applying these values in the formula:

$\text{Average Rate of Change} = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{-4 - (-8)}{1 - (-1)} = \frac{-4 + 8}{2} = \frac{4}{2} = 2$

Thus, the average rate of change is 2.

Would you like more details or have any questions about this? Here are some related questions to consider:

1. How is the average rate of change related to the slope of a secant line?
2. Can the average rate of change be negative?
3. How can we interpret the average rate of change graphically?
4. What is the difference between instantaneous rate of change and average rate of change?
5. How does the average rate of change apply to real-world problems?

Tip: The average rate of change is essentially the slope of the straight line connecting two points on the graph!