Question

A realtor has a budget of $4,180 to spend on their advertising. Each month, x, the realtor

spends $220 on different advertisements. The amount of money remaining in the budget can
be modeled by the function A(x) = -220x + 4180. Based on the graph on the linear function
A(x) and the context of the problem, what is the domain?

Answer 1

Answer:The domain of the function A(x) = -220x + 4180 represents the valid inputs or values of x in the context of the problem. In this case, the context is the monthly spending on advertisements for a realtor with a budget of $4,180.

Since the realtor's budget is fixed at $4,180, the domain of the function would be the range of valid values for x that represent the number of months the realtor can spend on advertisements.

In this situation, it would be reasonable to assume that the realtor cannot spend a negative number of months on advertisements. Additionally, the realtor cannot spend more months on advertisements than the total duration of their budget, which is determined by dividing the budget by the monthly spending.

To find the domain, we need to consider the restrictions mentioned above. Therefore, the domain would be:

x ≥ 0 and x ≤ 4180 / 220

Simplifying the inequality:

x ≥ 0 and x ≤ 19

So, the domain of the function A(x) would be the set of non-negative integers less than or equal to 19.