Question

rewrite the following radical function to identify its transformations from the parent graph.
$f(x) = \sqrt3{8x + 24}$

rewrite the function so that its transformations can be identified.
$f(x) = 2\sqrt3{x + 3}$
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: Recall Vertical Stretch/Compression Rule

For a function \( y = a \cdot f(x) \), if \( |a|>1 \), it's a vertical stretch by factor \( |a| \); if \( 0<|a|<1 \), it's a vertical compression. The parent cube - root function is \( y=\sqrt[3]{x} \). Our function is \( f(x) = 2\sqrt[3]{x + 3} \), where \( a = 2 \).

Step2: Determine Stretch/Compression Type

Since \( |2|=2>1 \), the function is vertically stretched. The factor of vertical stretch is the absolute value of the coefficient of the cube - root part, which is 2. So we choose option A and fill in 2.

Answer:

A. The given function is stretched vertically by a factor of 2 from the parent function.