Question

rewrite the function so that its transformations can be identified.\\(f(x)= 3sqrt3{x - 1}\\)\
describe any vertical stretch or compression. select the correct choice below, and, if necessary, fill in the answer box within your\
a. the given function is stretched vertically by a factor of 3 from the parent function.\\(\quad\\) (type a whole number.)\
b. the given function is compressed vertically by a factor of \\(\quad\\) from the parent function.\\(\quad\\) (type a whole number.)\
c. there is no stretch or compression.\
describe any horizontal translation. select the correct choice below, and, if necessary, fill in the answer box within your choice.\
a. the given function is translated \\(\quad\\) unit(s) to the left from the parent function.\\(\quad\\) (type a whole number.)\
b. the given function is translated \\(\quad\\) unit(s) to the right from the parent function.\\(\quad\\) (type a whole number.)\
c. there is no horizontal translation.

Explanation:

Step1: Identify parent function

The parent function is $f(x)=\sqrt[3]{x}$.

Step2: Analyze vertical transformation

The given function is $f(x)=3\sqrt[3]{x-1}$. A coefficient $a>1$ multiplying the parent function causes a vertical stretch by factor $a$. Here $a=3$.

Step3: Analyze horizontal translation

For a function $f(x-h)$, if $h>0$, it shifts the parent function right by $h$ units. Here the function is $\sqrt[3]{x-1}$, so $h=1$.

Answer:

For vertical stretch/compression:
A. The given function is stretched vertically by a factor of 3 from the parent function.

For horizontal translation:
B. The given function is translated 1 unit(s) to the right from the parent function.