Question

which describes how to graph $g(x) = \sqrt3{x - 5} + 7$ by transforming the parent function?

• translate the parent function 5 units to the left and 7 units up.
• translate the parent function 5 units to the right and 7 units up.
• translate the parent function 5 units down and 7 units to the right.
• translate the parent function 5 units up and 7 units to the right.

Explanation:

Step1: Recall transformation rules

For a function \( y = f(x - h)+k \), the horizontal translation is \( h \) units (right if \( h>0 \), left if \( h<0 \)) and vertical translation is \( k \) units (up if \( k>0 \), down if \( k<0 \)). The parent function for cube root is \( f(x)=\sqrt[3]{x} \). Here, \( g(x)=\sqrt[3]{x - 5}+7 \), so \( h = 5 \) and \( k = 7 \).

Step2: Determine translations

Since \( h = 5>0 \), horizontal translation is 5 units right. Since \( k = 7>0 \), vertical translation is 7 units up.

Answer:

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