1. **State the problem:** We need to find the average rate of change of the distance function from $x = -1$ to $x = 1$. 2. **Recall the formula for average rate of change:** $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ where $a = -1$ and $b = 1$. 3. **Identify the function values:** From the graph description: - At $x = -1$, the distance $f(-1)$ is on the left branch of the V-shaped graph. Since the vertex is at $(1,0)$ and the left branch passes through $(0,2)$, the graph is symmetric and linear on each side. The left branch rises as $x$ decreases from 0 to -1. The slope of the left branch can be found from points $(0,2)$ and $(1,0)$: $$m = \frac{0 - 2}{1 - 0} = \frac{-2}{1} = -2$$ Equation of left branch: $$f(x) = m(x - 1) + 0 = -2(x - 1) = -2x + 2$$ So, $$f(-1) = -2(-1) + 2 = 2 + 2 = 4$$ - At $x = 1$, the vertex point, $f(1) = 0$. 4. **Calculate the average rate of change:** $$\frac{f(1) - f(-1)}{1 - (-1)} = \frac{0 - 4}{1 + 1} = \frac{-4}{2} = -2$$ 5. **Interpretation:** The average rate of change from $x = -1$ to $x = 1$ is $-2$, meaning the distance decreases by 2 units per hour on average over this interval.