1. **State the problem:** Find the average rate of change of the function $f(x)$ from the point $(-1, 2)$ to the point $(3 \frac{1}{2}, 2)$. 2. **Recall the formula:** The average rate of change of a function between two points $(x_1, f(x_1))$ and $(x_2, f(x_2))$ is given by $$\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$$ 3. **Identify the points:** Here, $x_1 = -1$, $f(x_1) = 2$, $x_2 = 3 \frac{1}{2} = \frac{7}{2}$, and $f(x_2) = 2$. 4. **Substitute values into the formula:** $$\frac{f\left(\frac{7}{2}\right) - f(-1)}{\frac{7}{2} - (-1)} = \frac{2 - 2}{\frac{7}{2} + 1}$$ 5. **Simplify the denominator:** $$\frac{7}{2} + 1 = \frac{7}{2} + \frac{2}{2} = \frac{9}{2}$$ 6. **Calculate the average rate of change:** $$\frac{0}{\frac{9}{2}} = 0$$ 7. **Interpretation:** Since the function values at both points are the same, the average rate of change is zero, meaning the function did not increase or decrease between these points. **Final answer:** The function has an average rate of change of $0$.