Question

Trevon opens a checking account that he only uses to pay fixed bills, which are expenses that are the same each month, such as car loans or rent. The checking account has an initial balance of $1750 and Trevon deposits $925 each month. The balance of the account can be modeled by 𝑎⁡(𝑥)=1750+925⁢𝑥, where 𝑥 is the number of months since the account was opened. The total of Trevon’s fixed bills is modeled by 𝑏⁡(𝑥)=840⁢𝑥. Define and graph the function that represents the account balance after he pays his bills.

a. Identify and write a new function to represent the account balance.
b. Graph the function that represents the account balance after he pays the bill. state domain and range

Answer 1

a) Let c(x) be the balance after paying bills. Then
c(x) = a(x) − b(x) = (1750 + 925x) − 840x = 1750 + 85x.

b) Graph: the graph is a straight line with y‑intercept 1750 and slope 85 (rising 85 dollars per month). Example points: (0,1750), (1,1835), (2,1920), (3,2005).

Domain: x is the number of months since opening, so x ≥ 0 (more precisely x ∈ {0,1,2,…} if you restrict to whole months).
Range: c(x) ≥ 1750 (or as a discrete set {1750 + 85n | n = 0,1,2,…} if x is integer).