1. The problem states that the graph is a translation of the function $f(x) = \sqrt[3]{x}$. We need to write the function for the translated graph. 2. The original function is $f(x) = \sqrt[3]{x}$. 3. The graph is translated right by 6 units and down by 2 units. 4. Translation rules for functions: - Translating right by $h$ units: replace $x$ with $x - h$. - Translating down by $k$ units: subtract $k$ from the function. 5. Applying these translations to $f(x)$: $$f(x) = \sqrt[3]{x} \implies g(x) = \sqrt[3]{x - 6} - 2$$ 6. This means the new function is: $$\boxed{g(x) = \sqrt[3]{x - 6} - 2}$$ This matches the graph with the inflection point at $(6, -2)$, confirming the translation.