the volume of a rectangular cardboard box is modeled by the functions v (x) = (18-2x) (3-2x) x where x is the width

The given function of volume v (x) = (18-2x) (3-2x) x is true for certain boundaries of x which is mentioned below.

Step-by-step explanation:

The equation for the volume is represented as:

v (x) = (18-2x) (3-2x) x

As x represents the width, it cannot be negative or zero. X must be greater than 0. For the equation (18-2x), the term can't be negative or zero so,

18-2x > 0

or, 2x < 18

or, x < 9

For the term, 3-2x > 0

or, 2x < 3

or, x < 1.5

This develops the boundary for x as,

0 < x < 1.5