Question

use transformations to graph the function.
$m(x) = 6\sqrt3{x}$

Explanation:

Step1: Identify parent function

Parent function: $f(x)=\sqrt[3]{x}$

Step2: Identify transformation type

Vertical stretch by factor 6: $m(x)=6f(x)$

Step3: Transform key parent points

• For $x=-8$: $f(-8)=\sqrt[3]{-8}=-2$, so $m(-8)=6(-2)=-12$
• For $x=0$: $f(0)=\sqrt[3]{0}=0$, so $m(0)=6(0)=0$
• For $x=8$: $f(8)=\sqrt[3]{8}=2$, so $m(8)=6(2)=12$

Step4: Plot transformed points

Plot $(-8,-12)$, $(0,0)$, $(8,12)$, then draw a smooth curve through them, maintaining the shape of the parent cube root function, stretched vertically.

Answer:

The graph of $m(x)=6\sqrt[3]{x}$ is a vertical stretch by a factor of 6 of the parent cube root function $f(x)=\sqrt[3]{x}$, passing through points $(-8,-12)$, $(0,0)$, and $(8,12)$ with the characteristic S-shape of a cube root curve, scaled vertically.