1. The graph of \( f(x)=\sqrt{x} \) was transformed to create the graph of \( g(x)=-\sqrt{x-2}+1 \). What transformations took place to create the new graph?

To transform the graph of \( f(x) = \sqrt{x} \) into \( g(x) = -\sqrt{x-2} + 1 \), the following **three** transformations are applied in sequence: 1. **Horizontal Shift to the Right by 2 Units:** - **Transformation Applied:** Replace \( x \) with \( x - 2 \) inside the square root. - **Effect on Graph:** Moves the graph of \( f(x) \) two units to the right. - **Resulting Function:** \( \sqrt{x - 2} \) 2. **Reflection Across the X-axis:** - **Transformation Applied:** Multiply the entire square root expression by \(-1\). - **Effect on Graph:** Flips the graph upside down across the x-axis. - **Resulting Function:** \( -\sqrt{x - 2} \) 3. **Vertical Shift Upwards by 1 Unit:** - **Transformation Applied:** Add \( +1 \) to the entire expression. - **Effect on Graph:** Moves the graph one unit upward. - **Resulting Function:** \( -\sqrt{x - 2} + 1 \) **Summary of Transformations:** 1. **Right Shift:** 2 units right. 2. **Reflection:** Across the x-axis. 3. **Upward Shift:** 1 unit up. These combined transformations result in the graph of \( g(x) = -\sqrt{x-2} + 1 \). **Graphical Illustration:**  *(Note: Replace the image link with an appropriate graph illustrating the transformations if needed.)* **Final Answer:** First shift the graph right two units, then reflect it across the x‑axis, and finally move it up by one unit.