1. The problem is to identify the graph of the function $$f(x) = \sqrt{x + 4} + 2$$. 2. The function is a square root function with a horizontal shift and a vertical shift. 3. The general form of a square root function is $$f(x) = \sqrt{x - h} + k$$ where $h$ is the horizontal shift and $k$ is the vertical shift. 4. Here, $x + 4$ inside the square root means a horizontal shift to the left by 4 units (since $x + 4 = x - (-4)$). 5. The $+2$ outside the square root means a vertical shift upward by 2 units. 6. The domain of the function is where the expression inside the square root is non-negative: $$x + 4 \geq 0 \Rightarrow x \geq -4$$. 7. The starting point (vertex) of the graph is at $x = -4$, and the value of the function there is $$f(-4) = \sqrt{-4 + 4} + 2 = \sqrt{0} + 2 = 2$$. 8. So the graph starts at the point $(-4, 2)$ and moves upward to the right. 9. Comparing this with the three graphs: - Left graph starts near $(-5, 1)$, which does not match. - Center graph starts near $(-4, 3)$, close but the $y$-value is 3 instead of 2. - Right graph starts near $(0, 2)$, which does not match the domain start. 10. The center graph is closest to the expected start point $(-4, 2)$, but the $y$-value is slightly off. 11. Since the function starts at $(-4, 2)$, the correct graph is the one starting near $(-4, 2)$ and moving upward to the right. 12. Therefore, the center graph is the correct graph for $$f(x) = \sqrt{x + 4} + 2$$.