Question

rewrite the following radical function to identify its transformations from the parent graph
$f(x)=\sqrt3{27x - 27}$

rewrite the function so that its transformations can be identified.
$f(x)=3\sqrt3{x - 1}$

describe any vertical stretch or compression. select the correct choice below, and, if necessary, fill in the answer box within your choice.
\\(\bigcirc\\) a. the given function is stretched vertically by a factor of \\(\square\\) from the parent function.
( type a whole number )
\\(\bigcirc\\) b. the given function is compressed vertically by a factor of \\(\square\\) from the parent function.
( type a whole number )
\\(\bigcirc\\) c. there is no stretch or compression.

Explanation:

Step1: Factor radicand

$\sqrt[3]{27x-27} = \sqrt[3]{27(x-1)}$

Step2: Simplify cube root

$\sqrt[3]{27(x-1)} = \sqrt[3]{27} \cdot \sqrt[3]{x-1} = 3\sqrt[3]{x-1}$

Step3: Identify vertical stretch

For parent function $g(x)=\sqrt[3]{x}$, $f(x)=3g(x-1)$. The coefficient 3 indicates vertical stretch.

Answer:

A. The given function is stretched vertically by a factor of 3 from the parent function.