1. The problem is to identify the graph of the function $$f(x) = \sqrt{x + 3} + 1$$. 2. The function involves a square root, so the domain is where the expression inside the root is non-negative: $$x + 3 \geq 0 \Rightarrow x \geq -3$$. 3. The graph starts at the point where the inside of the root is zero: $$x = -3$$. 4. Calculate the starting point: $$f(-3) = \sqrt{-3 + 3} + 1 = \sqrt{0} + 1 = 1$$. 5. The graph should start at $(-3, 1)$ and increase as $x$ increases. 6. Check the points given for each graph: - Graph 1 starts near $(-2, 2)$ and goes through $(1, 4)$. - Graph 2 starts near $(1, 2)$ and goes through $(6, 5)$. - Graph 3 starts near $(-3, 2)$ and goes through $(3, 4)$. 7. Our function starts at $(-3, 1)$, so Graph 3 starting near $(-3, 2)$ is close but the y-value is off by 1. 8. Check the function value at $x = 1$: $$f(1) = \sqrt{1 + 3} + 1 = \sqrt{4} + 1 = 2 + 1 = 3$$. 9. Graph 1 goes through $(1, 4)$, which is higher than 3, so it does not match. 10. Graph 2 starts at $(1, 2)$, which is less than 3, so it does not match. 11. The function's starting point is at $(-3, 1)$, so the graph must start at $x = -3$ and $y = 1$. 12. None of the graphs exactly match the function, but Graph 3 is closest in domain start. 13. The correct graph should start at $(-3, 1)$ and increase to the right. 14. Therefore, the graph that best represents $$f(x) = \sqrt{x + 3} + 1$$ is Graph 3. Final answer: Graph 3.