Final answer:
The appropriate domain for the function representing the volume of an open-top box is between 1 and 5, which aligns with the physical constraints of the lengths of the cut-out squares needed to create the box.
Step-by-step explanation:
The question addresses the issue of finding an appropriate domain for a function that represents the volume of an open-top box in terms of the length of the cut-out squares used to make it. The domain of a function includes all the possible input values (x-values) for the function, and in the context of a physical problem like this one, the domain must represent realistic, physical constraints. When considering the size of cut-out squares for constructing an open-top box, the squares cannot have a negative length, and so negative values for x do not make sense. Also, if the cut-out length x is too large, specifically greater than the dimensions of the sides of the material used to make the box, it would not be possible to create the box. Therefore, the volume should be considered only for positive values of x that are less than the dimensions of the sides of the initial piece of material.
In summary, the more appropriate domain for the function V(x) would be between 1 and 5, assuming that x represents the length of the sides of the cut-out squares in inches and that the value of x must be less than the sides of the box material for it to form a box. This eliminates negative values and values too large to form a box. Hence, the answer is (d) Volume between 1 and 5.