Final answer:
The reasonable domain for the list price of a used car, represented by x, is the set of c) non-negative real numbers, allowing for any positive amount or zero, but excluding negative values.
Step-by-step explanation:
If x is the list price (in dollars) for a used car, a reasonable domain for x would be the set of non-negative real numbers. This includes all positive numbers and zero, reflecting the reality that a car cannot have a negative price, but it can be given away for free, hence the inclusion of zero. However, list prices are typically not expressed in fractions of a cent, so while x can be any non-negative real number, in practical scenarios it's often rounded to the nearest cent.
Option c) Non-negative real numbers is the best choice because it accommodates the possibility of a car being priced at zero dollars (given away for free) or any positive amount. Negative values for a list price would not make sense in a real-world context, and whole numbers would exclude valid prices that include cents. Moreover, while all positive real numbers would also be a potential domain, it excludes the possibility of a zero-priced vehicle, which is theoretically possible.