The problem asks for the average rate of change of the function $f(x)$ from $x = -2$ to $x = 4$, which can be interpreted as the slope of the secant line between these two points.

The formula for the average rate of change of a function $f(x)$ over an interval $[a, b]$ is:

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

Step 1: Identify the values of $f(x)$ at $x = -2$ and $x = 4$.

From the graph:

• $f(-2) = 4$
• $f(4) = 4$

Step 2: Apply the values to the formula.

Substitute $f(-2) = 4$, $f(4) = 4$, $a = -2$, and $b = 4$ into the formula:

$\text{Average Rate of Change} = \frac{f(4) - f(-2)}{4 - (-2)} = \frac{4 - 4}{4 + 2} = \frac{0}{6} = 0$

Final Answer:

The average rate of change of the function from $x = -2$ to $x = 4$ is 0.

Would you like more details or have any questions? Here are 5 related questions that expand on this topic:

1. What does the average rate of change tell us about the behavior of the function over an interval?
2. How does the average rate of change differ from the instantaneous rate of change?
3. Can the average rate of change be negative? If so, what does that signify?
4. How would you calculate the average rate of change if given an equation instead of a graph?
5. What can you infer about a function if its average rate of change over a certain interval is zero?

Tip: The average rate of change over an interval corresponds to the slope of the straight line connecting the endpoints of the graph over that interval (the secant line).