Describing Transformations of Radical Functions

We know the following about translations up and to the right. $$\begin{array}{r}\text{translation h units horizontally:}f(x-h)\\ \text{translation k units vertically:}f(x)+k\end{array}$$ If we compare the transformed function with its parent function $y=a\sqrt[3]{x},$ we notice one of each transformation. $$\begin{array}{rl}\text{translation h units horizontally:}& y=a\sqrt[3]{x-h}+k\\ \text{translation k units vertically:}& y=a\sqrt[3]{x-h}+k\end{array}$$