Question

the table represents the cost for oranges in mr. nguyens store.
number of oranges 1 2 3 4
cost in cents 20 40 60 80
in this situation, cost is a function of the number of oranges. which one of the following sets represents the domain of this function?
{21,42,63,84,...} {1,2,3,4,...}
{1,4,20,80,...} {20,40,60,80,...}

Explanation:

Step1: Recall Domain Definition

The domain of a function is the set of all input values (independent variable). Here, the independent variable is the number of oranges.

Step2: Identify Input Values

From the table, the number of oranges (input) values are 1, 2, 3, 4, and in a real - world context of buying oranges, it can be any positive integer (since you can buy 1, 2, 3, 4, ... oranges). So the domain should be the set of positive integers starting from 1.
Looking at the options:

• Option \(\{21, 42, 63, 84, \dots\}\): These are not related to the number of oranges.
• Option \(\{1, 2, 3, 4, \dots\}\): This represents the set of possible number of oranges (input values), so it is the domain.
• Option \(\{1, 4, 20, 80, \dots\}\): This is a mix of number of oranges and cost values, not just the input values.
• Option \(\{20, 40, 60, 80, \dots\}\): These are the cost values (output values, range), not the domain.

Answer:

\(\{1, 2, 3, 4, \dots\}\) (the second option among the given choices)