Question

Determine the range of the function modeled by the equation. In late August, Ellis is given some stamps by his uncle. On September 1, he begins to buy new stamps to add to his collection. The number of stamps in his collection can be determined using the equation f(x)=40x+57 , in which x indicates the number of weeks that have gone by since September 1 and f(x) represents the total number of stamps in his collection. However, Ellis loses interest in his collection after five weeks and stops purchasing new stamps, invalidating the ability of the function to describe the number of stamps he has after that point. How can the range of this real-world function be described using inequality symbols?(

Answer 1

Domain: 0 ≤ x ≤ 5 (weeks).
So the range is 57 ≤ f(x) ≤ 257 because f(0) = 57 and f(5) = 40(5)+57 = 257.

(If x is restricted to integer weeks 0,1,2,3,4,5 the range is the discrete set {57,97,137,177,217,257}.)