1. The problem asks to identify which function corresponds to the given graph. 2. The graph is described as an increasing cube-root-shaped curve with an inflection point around $(2, -3)$. 3. The general form of the cube root function is $$f(x) = \sqrt[3]{x - h} + k$$ where $(h, k)$ is the inflection point (the point where the curve changes concavity). 4. Since the inflection point is at $(2, -3)$, the function must be of the form $$f(x) = \sqrt[3]{x - 2} - 3$$ 5. Comparing this with the options: - A: $f(x) = \sqrt[3]{x + 2} - 3$ has inflection at $(-2, -3)$ - B: $f(x) = \sqrt[3]{x - 2} - 3$ has inflection at $(2, -3)$ - C: $f(x) = \sqrt[3]{x + 3} - 2$ has inflection at $(-3, -2)$ - D: $f(x) = \sqrt[3]{x - 3} - 2$ has inflection at $(3, -2)$ 6. Therefore, the correct function is option B. **Final answer:** $$f(x) = \sqrt[3]{x - 2} - 3$$