1. The problem is to identify the graph of the function $$f(x) = \sqrt{x - 5} - 1$$. 2. The function involves a square root, so the domain is where the expression inside the root is non-negative: $$x - 5 \geq 0 \Rightarrow x \geq 5$$. 3. The graph starts at the point where the inside of the root is zero, i.e., at $$x=5$$. At this point, $$f(5) = \sqrt{5-5} - 1 = 0 - 1 = -1$$. 4. The graph will increase slowly to the right because the square root function grows slowly. 5. So the graph should start at the point $$(5, -1)$$ and increase to the right. 6. Checking the descriptions: - Graph 1 starts just right of $$x=5$$ on the x-axis but at $$y=0$$, which does not match the starting point $$y=-1$$. - Graph 2 starts near $$x=5$$ and $$y\approx -1.5$$, close to $$-1$$, and moves gently upwards to the right. - Graph 3 starts near $$x=-5$$, which is outside the domain. 7. Therefore, the correct graph is Graph 2. Final answer: Graph 2 matches the function $$f(x) = \sqrt{x - 5} - 1$$.