1. **State the problem:** We need to shift the function $y=\sqrt{x}$ 2 units to the right and 1 unit down. 2. **Recall the transformation rules:** - Shifting a function $f(x)$ to the right by $h$ units is done by replacing $x$ with $x - h$. - Shifting a function down by $k$ units is done by subtracting $k$ from the function. 3. **Apply the horizontal shift:** $$y=\sqrt{x} \to y=\sqrt{x-2}$$ 4. **Apply the vertical shift:** $$y=\sqrt{x-2} - 1$$ 5. **Final transformed function:** $$y=\sqrt{x-2} - 1$$ This means the graph of $y=\sqrt{x}$ moves 2 units right and 1 unit down, resulting in the new function $y=\sqrt{x-2} - 1$.