The prinipal of Hamilton Middle School rented a shaved-ice machine for the annual end-of-year school pinic. The machine shaves 6 pounds of ice per minutines, The funtion F(n) repsents the amounts of ice, in pounds, the machine has shaved after n mintues of use. What is the domain of F(n)?

The function \( F(n) \) represents the amount of ice, in pounds, that the machine has shaved after \( n \) minutes of use. Since the machine shaves 6 pounds of ice per minute, the function \( F(n) \) can be written as:

\[
F(n) = 6n
\]

The domain of the function \( F(n) \) is the set of all possible values of \( n \) (the time in minutes) for which \( F(n) \) is defined. 

In this context:
- \( n \) represents time, so it must be non-negative.
- Therefore, \( n \) can be any non-negative real number.

Thus, the domain of \( F(n) \) is:

\[
n \geq 0
\]

In interval notation, the domain is:

\[
[0, \infty)
\]

This means that the function \( F(n) \) is defined for all \( n \) starting from 0 and extending to any positive value.

Would you like more details or have any questions?

Here are five related questions you might find helpful:
1. How much ice will the machine shave after 10 minutes?
2. If the machine operates for 15 minutes, what will the output be in pounds?
3. What would the function look like if the machine shaved 8 pounds of ice per minute?
4. Is there a maximum amount of ice the machine can shave in a certain time period?
5. What is the range of the function \( F(n) \)?

**Tip:** When dealing with time-based functions, always ensure that the domain reflects that time cannot be negative.

Explore the domain of the function F(n) = 6n, which represents the amount of ice shaved by a machine after n minutes. Learn about linear functions and their domains in this detailed explanation suitable for Grades 7-9 students.

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