Answer:
The translation corresponds to : [tex]g(x)=\sqrt[3]{x-4}[/tex]
which is the first option in your list of possible answers
Step-by-step explanation:
Notice that this new function's graph responds to a horizontal translation to the right of the original graph of [tex]f(x)=\sqrt[3]{x}[/tex]. Notice that the crossing of the x-axis, which for f(x) is at the origin (0, 0), has now moved to the point (4,0), which means a translation to the right in exactly 4 units.
Recall that horizontal translations are performed by subtracting from the independent variable (x) , the number of units you move (in this case 4)
Therefore the new function should look like:
[tex]g(x)=\sqrt[3]{x-4}[/tex]