Question

Tyler finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of the square cutouts used to make it. This is the graph Tyler gets if he allows x to take on any value between -1 and 7. What would be a more appropriate domain for Tyler to use instead?

A) 0 ≤ x ≤ 7
B) -1 ≤ x ≤ 7
C) x > 0
D) x > -1

Answer 1

The most appropriate domain for the function that gives the volume of an open-top box, in terms of square cutouts used to make it, is where x is strictly greater than zero, as this represents the physical restriction of cutout lengths.

Step-by-step explanation:

The question asks what would be a more appropriate domain for Tyler to use for the function V(x) that gives the volume of an open-top box, when the variable x represents the length of square cutouts used to make it. Considering that the length of a cutout cannot be negative, as that would not make physical sense, Tyler must choose a domain that includes only non-negative values.

As such, the length also cannot be zero, because then there would be no box. Therefore, the only sensible domain would be where x is strictly greater than zero.

Hence, the most appropriate domain for Tyler to use is C) x > 0.