Answer: Four units to the right and three units up from [tex]\sqrt[3]{x}[/tex]
Step-by-step explanation:
1. By definition, a parent function is the simplest form of a function.
2. You have the parent function [tex]\sqrt[3]{x}[/tex],
3. The function [tex]\sqrt[3]{(x-4)}+3[/tex] is the translation of the parent function shown above.
4. The subtraction -4 inside of the cube root indicates the horizontal shift to the right from the parent function and the addtion +3 outside of the cube root indicates the vertical shift up from the parent function.
5. Therefore, the description of the translation is: Four units to the right and three units up from [tex]\sqrt[3]{x}[/tex]