Given the parent cube root function:
[tex]y=\sqrt[3]{x}[/tex]
The graph shown is a translation of the parent cube-root function, let's determine the graphed function g(x).
We have the parent cube-root graph below:
We can see the translated function moves 4 units to the right.
Now, to write the function, apply the transformation rules for functions.
After a translation 4 units to the right, the function will be:
[tex]g(x)=\sqrt[3]{x-4}[/tex]
Therefore, the equation which represents g(x) is:
[tex]g(x)=\sqrt[3]{x-4}[/tex]
ANSWER:
[tex]g(x)=\sqrt[3]{x-4}[/tex]
