1. The problem is to identify the graph of the function $$f(x) = \sqrt{x} + 2 - 4$$. 2. First, simplify the function: $$f(x) = \sqrt{x} + 2 - 4 = \sqrt{x} - 2$$ 3. The function is a square root function shifted vertically downward by 2 units. 4. The domain of $$f(x)$$ is $$x \geq 0$$ because the square root is only defined for non-negative values. 5. The range of $$f(x)$$ is $$y \geq -2$$ since the smallest value of $$\sqrt{x}$$ is 0, and subtracting 2 shifts the graph down. 6. The graph starts at the point $$(0, -2)$$ and increases slowly to the right. 7. Comparing with the given graphs: - Graph 1 starts near $(-1, -4)$ which is outside the domain. - Graph 2 starts near $(-2, 0)$ which is outside the domain. - Graph 3 starts near $(-4, -6)$ which is outside the domain. 8. None of the graphs start exactly at $$(0, -2)$$, but Graph 1 passes through $x=0$$ near $$y=-4$$ which is too low. 9. Graph 2 starts near $(-2, 0)$$ which is invalid domain. 10. Graph 3 starts near $(-4, -6)$$ which is invalid domain. 11. Since the function domain is $$x \geq 0$$ and range $$y \geq -2$$, the graph must start at $$(0, -2)$$ and increase. 12. The best match is Graph 1, but shifted vertically by 2 units down from $$\sqrt{x} + 2$$. 13. Therefore, the graph of $$f(x) = \sqrt{x} - 2$$ is Graph 1 (bottom-left).