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

You want to know what transformation maps $3 \sqrt{x}$ onto $3 \sqrt{x-4} +3$.

Note $f(x)=3\sqrt{x}$ so $f(x-4)=3 \sqrt{x-4}$ so $f(x-4)+3= \sqrt{x-4}+3$.

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

Answer 2

Answer:

Step-by-step explanation:

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