To find the average rate of change of the function $h(x)$ between $x = -3$ and $x = 1$, we use the formula for the average rate of change:

$\text{Average rate of change} = \frac{h(b) - h(a)}{b - a}$ where $a = -3$ and $b = 1$.

From the graph:

• At $x = -3$, the function value $h(-3) = 0$.
• At $x = 1$, the function value $h(1) = -4$.

Now, apply these values to the formula:

$\text{Average rate of change} = \frac{h(1) - h(-3)}{1 - (-3)} = \frac{-4 - 0}{1 + 3} = \frac{-4}{4} = -1$

Thus, the average rate of change is $-1$.

Would you like further clarification or more details?

Here are 5 related questions:

1. What does the average rate of change tell us about the behavior of the function between two points?
2. How does the average rate of change relate to the slope of the secant line?
3. What is the difference between instantaneous rate of change and average rate of change?
4. Can the average rate of change be positive, and what does that signify graphically?
5. How can we estimate the function's maximum or minimum from a graph?

Tip: The average rate of change over an interval is simply the slope of the line connecting the two points on the graph at the boundaries of that interval.