Question

The house-numbers on a certain street go from 1 to 88. The function B(n) models the type of the building whose number is n according to the following key:

Building type Function output
Residential building 0
Commercial building 1
Government building 2
Other 3


Which number type is more appropriate for the domain of B?
A. Integers
B. Real numbers

Answer 1

The function B(n) models building types based on house numbers. The domain should consist of integers because house numbers are whole numbers. Therefore, the correct option for the domain is b). B(n) is an integer.

Step-by-step explanation:

The function B(n) models the type of a building by providing an output that corresponds to a certain type of building, where n stands for the house number. When we consider the domain for this function, which consists of house numbers on a street that range from 1 to 88, we are looking at whole numbers that represent these specific addresses. Thus, the most appropriate number type for the domain of B(n) would be integers, as house numbers do not contain fractions or decimals and must be whole numbers.

Real numbers include all rational and irrational numbers, spanning from negative infinity to positive infinity, including fractions and decimal numbers. However, in our case, house numbers do not make sense as fractions or decimal points, and hence, real numbers are not suitable for this context. By examining the domain of the function B(n) which pertains to house numbers, and understanding that house numbers are discrete and cannot be a fraction or decimal, we conclude that the correct option for the function's domain is integers, not real numbers.