Question

fva 25 - 26: algebra ii q3
cubic and cube root functions and equations
which describes how to graph $g(x) = \sqrt3{x-3} + 7$ by transforming the parent function?
translate the parent function 3 units to the left and 7 units up.
translate the parent function 3 units to the right and 7 units up.
translate the parent function 3 units down and 7 units to the right.
translate the parent function 3 units up and 7 units to the right.

Explanation:

Step1: Identify horizontal translation

For a cube root function of the form $\sqrt[3]{x - h}$, $h$ shifts the parent function $\sqrt[3]{x}$ horizontally. Here, $h=5$, so shift right 5 units.

Step2: Identify vertical translation

For a function of the form $\sqrt[3]{x - h} + k$, $k$ shifts the function vertically. Here, $k=7$, so shift up 7 units.

Answer:

Translate the parent function 5 units to the right and 7 units up.