Final answer:
The function H(y) represents the leading home runs by season for a specific time range, where the domain should consist of whole years, making whole numbers the most appropriate choice for the domain of H.
Step-by-step explanation:
The function H(y) models the leading number of home runs for season y of the National League between the years 2000-2010. Considering that seasons are counted in whole years, the most appropriate type of number for the domain of H would be whole numbers. This is because the domain represents the years, which are discrete and cannot have fractional or decimal values in this context.
The possible values of y are 2000, 2001, 2002, ... , 2010, which are all whole numbers. Real numbers or rational numbers would not be suitable as they include fractions and decimals, which do not make sense in the context of counting years. Integers would not be entirely incorrect but whole numbers are more appropriate as they are positive and include zero, aligning with the traditional way years are enumerated.