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

Explanation:

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

So, the volume of the box,
`x = a * a * 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.