1. The problem asks to sketch the graph of the equation $$y = 3 - \sqrt{x + 1}$$ by transforming the graph of $$y = \sqrt{x}$$. 2. Start with the base graph $$y = \sqrt{x}$$, which is the square root function starting at the origin (0,0) and increasing slowly. 3. The expression inside the square root is $$x + 1$$, which means the graph is shifted to the left by 1 unit. So the starting point moves from (0,0) to (-1,0). 4. The negative sign in front of the square root, $$-\sqrt{x + 1}$$, reflects the graph across the x-axis. This flips the graph upside down. 5. The +3 outside the square root shifts the entire graph up by 3 units. 6. Combining these transformations, the graph of $$y = 3 - \sqrt{x + 1}$$ starts at (-1,3) and decreases as $$x$$ increases, following the reflected square root shape. 7. To confirm, use a graphing utility to plot $$y = 3 - \sqrt{x + 1}$$ and verify the shape matches the described transformations. Final answer: The graph is the reflection of $$y=\sqrt{x}$$ about the x-axis, shifted left by 1 and up by 3.