If the parent function is 3 square root x, describe the translation of the function y=3 square root x-4 +3

You want to know what transformation maps  onto .

Note so  so .

We just analyse the function to see the translations. f(x-4) corresponds to a horizontal translation 4 units in the positive x direction. f(x)+3 corresponds to a vertical translation 3 units in the positive y direction.

So overall, the parent function moves 4 units right and 3 units up. This is a translation by the vector .