Question

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

Answer 1

Explanation:

Four units to the rights and three units up from ^3 square x.

Answer 2

You want to know what transformation maps
`3 √(x)` onto
`3 √(x-4) +3`.

Note
`f(x)=3√(x)` so
`f(x-4)=3 √(x-4)` so
`f(x-4)+3= √(x-4)+3`.

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
`\left[\begin{array}{r}4&3\end{array}\right]`.