1. The problem is to identify the graph of the function $f(x) = \sqrt{x + 4} - 4$. 2. The function is a square root function shifted horizontally and vertically. The general form is $f(x) = \sqrt{x - h} + k$, where $(h, k)$ is the shift. 3. Here, $f(x) = \sqrt{x + 4} - 4$ means the graph is shifted left by 4 units (since $x + 4 = x - (-4)$) and down by 4 units. 4. The domain is $x + 4 \geq 0 \Rightarrow x \geq -4$. 5. The starting point (vertex) of the graph is at $x = -4$, so $f(-4) = \sqrt{-4 + 4} - 4 = 0 - 4 = -4$. 6. The graph starts at $(-4, -4)$ and increases slowly as $x$ increases. 7. Checking the given graphs: - Graph 1 starts near $(-4, 1)$, which is incorrect. - Graph 2 starts near $(0, 1)$, which is incorrect. - Graph 3 starts near $(-4, -4)$, which matches our function's vertex. 8. Therefore, the correct graph is the third one (bottom-right). Final answer: The graph of $f(x) = \sqrt{x + 4} - 4$ is the third graph (bottom-right).