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

Explanation:

Step1: Recall function - translation rules

For a function (y = f(x)), (y=f(x - h)+k) is a transformation of the parent - function. Here, (h) represents horizontal translation and (k) represents vertical translation.

Step2: Identify (h) and (k) values

The given function is (g(x)=\sqrt[3]{x - 5}+7), comparing it with the general form (y = f(x - h)+k) of a transformed function (where the parent function of (g(x)) is (y=\sqrt[3]{x})), we have (h = 5) and (k = 7).

Step3: Determine the translation

When (h>0), the graph of the parent function (y = f(x)) is translated (h) units to the right. When (k>0), the graph of the function (y = f(x - h)) is translated (k) units up. Since (h = 5) and (k = 7), the parent function (y=\sqrt[3]{x}) is translated 5 units to the right and 7 units up.

Answer:

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