1. The problem is to identify the graph of the function $f(x) = \sqrt{x - 2} + 3$. 2. The general form of a square root function is $f(x) = \sqrt{x - h} + k$, where $(h, k)$ is the starting point (or vertex) of the graph. 3. For $f(x) = \sqrt{x - 2} + 3$, the starting point is at $(2, 3)$ because the expression inside the square root must be non-negative: $x - 2 \geq 0 \Rightarrow x \geq 2$. 4. The graph starts at $(2, 3)$ and increases gradually to the right since the square root function increases as $x$ increases. 5. Comparing the descriptions: - Bottom-left graph starts near $(2, 3)$ and increases gradually. - Bottom-center graph also starts near $(2, 3)$ and increases gradually. - Bottom-right graph starts near $(-1, 3)$, which does not match our function. 6. Both bottom-left and bottom-center graphs start at $(2, 3)$, but their y-axis ranges differ slightly. 7. Since the function $f(x) = \sqrt{x - 2} + 3$ has a minimum value of 3 at $x=2$ and increases upwards, the graph must start at $(2, 3)$ and go upwards. 8. The bottom-left graph's y-axis range is from $-2$ to $7$, which includes values below 3, inconsistent with the function's minimum. 9. The bottom-center graph's y-axis range is from $-1$ to $8$, also including values below 3, but the description says the curve starts near $(2, 3)$ and increases gradually. 10. Both graphs could be possible, but the key is the starting point and the range. 11. The bottom-right graph is incorrect because it starts at $(-1, 3)$, which does not satisfy the domain $x \geq 2$. 12. Therefore, the correct graph is either bottom-left or bottom-center, but since the function's minimum value is 3, the graph should not go below 3. 13. The bottom-center graph's y-axis range includes values below 3, but the curve starts at $(2, 3)$ and increases, so the curve itself does not go below 3. 14. The bottom-left graph's y-axis range includes values below 3, but the curve starts at $(2, 3)$ and increases. 15. Both graphs could be correct, but the problem states the blue curve starts near $(2, 3)$ and increases gradually. 16. The best match is the bottom-center graph. Final answer: The graph of $f(x) = \sqrt{x - 2} + 3$ is the bottom-center graph.