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The question asks for the *average rate of change* of the function \( f(x) \) on the interval \( -4 \leq x \leq 0 \). To solve this, we need to use the formula for the average rate of change between two points:

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

Here, \( a = -4 \) and \( b = 0 \). Now, we need to find the corresponding \( y \)-values from the graph for \( x = -4 \) and \( x = 0 \).

1. From the graph, when \( x = -4 \), it looks like \( f(-4) = 0 \).
2. When \( x = 0 \), it looks like \( f(0) = -8 \).

Now we can apply the formula:

\[
\text{Average Rate of Change} = \frac{f(0) - f(-4)}{0 - (-4)} = \frac{-8 - 0}{4} = \frac{-8}{4} = -2
\]

Thus, the average rate of change of \( f(x) \) on the interval \( -4 \leq x \leq 0 \) is \( -2 \).

Would you like more details or have any questions about this? Here are five related questions to expand your understanding:

1. What is the average rate of change over the interval \( -6 \leq x \leq -2 \)?
2. How would you compute the instantaneous rate of change at a specific point on the graph?
3. What is the significance of a negative average rate of change?
4. How would you interpret a zero average rate of change in terms of the graph?
5. How does the average rate of change relate to the slope of a secant line?

**Tip:** The average rate of change is equivalent to the slope of the secant line that connects the two points on the graph.

What is the average rate of change of the function f(x) on the interval -4 ≤ x ≤ 0?

This problem involves calculating the average rate of change for a function on the interval -4 ≤ x ≤ 0 using its graph. Learn the step-by-step solution and understand how to apply the formula for average rate of change.

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