To find the average rate of change of the function between $x = -1$ and $x = 1$, we need to use the formula for the average rate of change between two points $(x_1, y_1)$ and $(x_2, y_2)$:

$\text{Average rate of change} = \frac{y_2 - y_1}{x_2 - x_1}$

In this case:

• $x_1 = -1$ and $x_2 = 1$.
• We need the corresponding $y$-values from the graph for $x = -1$ and $x = 1$.

Reading from the graph:

• When $x = -1$, $y = 2$.
• When $x = 1$, $y = -2$.

Now, apply the formula:

$\text{Average rate of change} = \frac{-2 - 2}{1 - (-1)} = \frac{-4}{2} = -2$

Thus, the average rate of change of the function between $x = -1$ and $x = 1$ is -2.

Would you like more details or have any questions?

Related questions:

1. What does the average rate of change represent in terms of the graph's behavior?
2. How would the average rate of change differ if calculated over a different interval?
3. Can the average rate of change be the same as the instantaneous rate of change at a specific point?
4. How is the average rate of change connected to the slope of a secant line?
5. What are the key differences between the average rate of change and the derivative?

Tip:

The average rate of change is simply the slope of the secant line connecting two points on the graph over the given interval.