Every Saturday, Heather goes mountain biking. It takes Heather 32 minutes to bike 6 miles. The distance is a function of the time. Which is a reasonable range in the context of the problem?

1. 0 ≤ f (t) ≤ 6

2. 0 ≤ f (t) ≤ 32

3. 6 ≤ f (t) ≤ 32

4. 12 ≤ f (t) ≤ 24

To answer the problem above, we must interpret each given ranges in words.

1. If the time is greater than or equal to zero, the distance would be less than or equal to 6 miles.

2. If the time is less than or equal to 32 minutes, the distance would be greater than or equal to 0 miles

3. If the time is less than or equal to 32 minutes, the distance would be greater or equal to 6 miles

4. If the time is less than or equal to 24 minutes, the distance would be greater or equal to 12 miles.

The reasonable range is No. 2.

Since distance is a function of time, then the range must be the possible time that Heather could spend with her mountain bike.

Given that she can travel for period 32 minutes and that there can be no negative time. The answer is:

2. 0 ≤ f (t) ≤ 32