Question

Linear Functions Quick Check
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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?(1 point)
Responses

57≤y≤257
57 less-than-or-equal-to y less-than-or-equal-to 257

−∞<y<257
negative infinity less-than y less-than 257

57<y<257
57 less than y less than 257

40<y<57
40 less than y less than 57
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Answer 1

To determine the range of the function \( f(x) = 40x + 57 \) for \( x \) values from 0 to 5 (inclusive), we need to calculate the minimum and maximum values of \( f(x) \):

1. When \( x = 0 \):
\[
f(0) = 40(0) + 57 = 57
\]

2. When \( x = 5 \):
\[
f(5) = 40(5) + 57 = 200 + 57 = 257
\]

So, as \( x \) varies from 0 to 5, \( f(x) \) varies from 57 to 257. Therefore, the range of the function can be described as:

\[
57 \leq y \leq 257
\]

The correct response is:
**57 ≤ y ≤ 257**