1. **State the problem:** Duncan is transforming point $S(1,0)$ by translating it down 3 units, then reflecting over the x-axis. We need to check if Duncan's work is correct. 2. **Translation down 3 units:** Moving a point down 3 units subtracts 3 from the $y$-coordinate. $$S(1,0) \to S'(1,0-3) = S'(1,-3)$$ 3. **Reflection over the x-axis:** Reflecting over the x-axis changes the sign of the $y$-coordinate but keeps the $x$-coordinate the same. $$S'(1,-3) \to S''(1,-(-3)) = S''(1,3)$$ 4. **Check Duncan's work:** Duncan's final point is $I''(-1,-3)$ which means he changed the $x$-coordinate from 1 to -1 and kept $y=-3$. 5. **Identify the mistake:** Changing $x$ from 1 to -1 is a reflection over the y-axis, not the x-axis. 6. **Conclusion:** Duncan reflected over the y-axis instead of the x-axis after translating down 3 units. **Final answer:** Duncan reflected over the y-axis instead of the x-axis.