1. The problem asks to describe the translations that transform the graph of $f(x)=\sqrt[3]{x}$ into the graph of $j(x)=\sqrt[3]{x-2}+3$. 2. The general form for horizontal and vertical translations of a function $f(x)$ is: $$g(x) = f(x - h) + k$$ where $h$ is the horizontal shift and $k$ is the vertical shift. 3. In $j(x)=\sqrt[3]{x-2}+3$, we identify $h=2$ and $k=3$. 4. A positive $h$ means the graph shifts $h$ units to the right. 5. A positive $k$ means the graph shifts $k$ units up. 6. Therefore, the graph of $f(x)$ is shifted 2 units right and 3 units up to get $j(x)$. 7. From the options given, the correct translations are: - D. shift the graph of $f(x)$ 2 units right - B. shift the graph of $f(x)$ 3 units up Final answer: The graph is shifted 2 units right and 3 units up.