Question

4.00 per gallon. store b sells a container of fuel for $4.00 each. the cost of fuel at other store can be modeled by the function c(n) = 4n, where n is the number of gallons of fuel for store a and n is the number of containers of fuel at store b. the domain of c(n) = 4n is all real numbers. for each store, drag all the additional restrictions needed on values of n for c(n) to model each situation.
store a:
numbers greater than zero
numbers greater than or equal to zero
numbers less than zero
integer values only
store b:
numbers greater than 4
numbers greater than 4

Explanation:

Step1: Analyze the context

The problem is about the cost function \( c(n) = 4n \) where \( n \) is the number of containers of fuel. In real - world scenarios, the number of containers cannot be negative (since you can't have a negative number of containers) and it should be a non - negative integer (you can't buy a fraction of a container in most cases, and the number of containers should be at least 0). Also, if there are additional constraints from the store (like Store A or Store B having limits, but from the general context of the number of containers), we first consider the basic constraints on \( n \).

Step2: Determine valid restrictions

• The number of containers \( n \) cannot be negative, so \( n\geq0 \) (numbers greater than or equal to zero). Also, the number of containers should be a whole number (integer values only), because you can't have a fraction of a container. For example, you can't buy 1.5 containers in a typical fuel - container buying scenario. The "numbers less than zero" is invalid because you can't have a negative number of containers. "Numbers greater than zero" is too restrictive because you can buy zero containers (if you don't need fuel). "Numbers greater than 4" is not a general restriction unless specified by the store, and the problem is about general restrictions for the function to model the situation.

Answer:

The valid restrictions for \( n \) in the function \( c(n)=4n \) (where \( n \) is the number of containers of fuel) are "numbers greater than or equal to zero" and "integer values only". If we have to pick from the given options (assuming the options are the ones on the left: numbers greater than zero, numbers greater than or equal to zero, numbers less than zero, integer values only), the correct restrictions are "numbers greater than or equal to zero" and "integer values only". If we consider the most basic and necessary ones, "numbers greater than or equal to zero" (since you can have zero containers, meaning you buy no fuel) and "integer values only" (since the number of containers must be a whole number) are the key restrictions.