Question

A company ships coffee mugs using boxes in the shape of cubes. The function g(x) = the cube root of x gives the side length, in inches, for a cube with a volume of x cubic inches. Suppose the company decides to double the volume of the box. Which graph represents the new function?

Answer 1

Step-by-step explanation:

Initially, let the side of the cubical box is $a$ inches,

So, the volume of the box, $x = a \times a \times a= a ^3$.

Given that $g(x)=\sqrt[3]{x} =\sqrt[3]{a^3}$

$\Rightarrow g(x)=a \; \cdots (i)$

On doubling the volume of the box, the new volume is $2x$.

So, $g(x)=\sqrt[3]{2x} =\sqrt[3]{2a^3}$

$\Rightarrow g(x)=\sqrt[3]{2} a \; \cdots (i)$

As $\sqrt[3]{2} >1$, so the graph of  $g(x)=\sqrt[3]{2} a$ will be above of the $g(x)=a$ as shown in the graph.