1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $-6 \leq x \leq -2$. 2. **Recall the formula:** The average rate of change of a function $f(x)$ over an interval $[a,b]$ is given by $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ This formula calculates the slope of the secant line connecting the points $(a, f(a))$ and $(b, f(b))$ on the graph. 3. **Identify values from the problem:** Here, $a = -6$ and $b = -2$. From the graph description: - $f(-6)$ is just above 10, so we approximate $f(-6) \approx 11$. - $f(-2)$ is roughly 0. 4. **Apply the formula:** $$\frac{f(-2) - f(-6)}{-2 - (-6)} = \frac{0 - 11}{-2 + 6} = \frac{-11}{4}$$ 5. **Simplify the fraction:** $$\frac{-11}{4} = -2.75$$ 6. **Interpretation:** The average rate of change of $f(x)$ on the interval $[-6, -2]$ is $-2.75$. This means that on average, the function decreases by 2.75 units in $y$ for each 1 unit increase in $x$ over this interval.