1. **State the problem:** We need to identify the graph of the function $$f(x) = \sqrt{x} + 1 - 2$$. 2. **Rewrite the function:** Simplify the expression inside the function: $$f(x) = \sqrt{x} + 1 - 2 = \sqrt{x} - 1$$ 3. **Analyze the function:** The function is a square root function shifted down by 1 unit. 4. **Determine the domain:** Since the square root function requires the radicand to be non-negative, $$x \geq 0$$ 5. **Find the starting point:** At $$x=0$$, $$f(0) = \sqrt{0} - 1 = 0 - 1 = -1$$ 6. **Check the behavior:** As $$x$$ increases, $$\sqrt{x}$$ increases, so $$f(x)$$ increases starting from $$-1$$. 7. **Compare with graphs:** - Graph 1 starts near $$y=1$$ at $$x=1$$ and rises to about $$y=6$$ at $$x=8$$. - Graph 2 starts near $$y=1$$ at $$x=1$$ and rises to about $$y=3.5$$ at $$x=8$$. - Graph 3 starts near $$y=-2$$ at $$x=1$$ and rises to about $$y=3$$ at $$x=7$$. Since our function starts at $$y=-1$$ when $$x=0$$ and increases gradually, the closest match is Graph 3, which starts near $$-2$$ and rises to about $$3$$. **Final answer:** The graph of $$f(x) = \sqrt{x} - 1$$ corresponds to Graph 3.