Let's analyze the given statements to see which ones can be supported by the function $D(t)$, representing the traveler's distance from home at time $t$:

1. "The starting distance, at 0 hours, is 300 miles."

   • This means that $D(0) = 300$. This can represent an initial condition, so it's a plausible option.

2. "At 2 hours, the traveler is 725 miles from home."

   • This statement gives $D(2) = 725$. This is another valid distance at a specific time, so it is a plausible option.

3. "At 2.5 hours, the traveler is still moving farther from home."

   • This statement suggests that $D(t)$ is increasing at $t = 2.5$, meaning the traveler is still moving away. This describes a potential trend in the function, and could be plausible if the function is increasing at that point.

4. "At 3 hours, the distance is constant, at 875 miles."

   • A constant distance means the traveler has stopped moving at this point, i.e., $D(t) = 875$ for $t \geq 3$. If this holds for the function, it could be a possible option.

5. "The total distance from home after 6 hours is 1,062.5 miles."

   • This gives $D(6) = 1,062.5$, a specific value for the distance after 6 hours, which seems reasonable.

Conclusion:

Based on this, the three most plausible options are:

• The starting distance, at 0 hours, is 300 miles.
• At 2 hours, the traveler is 725 miles from home.
• The total distance from home after 6 hours is 1,062.5 miles.

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Do you want details on how to derive the function? Let me know if you have any questions.

Related questions:

1. What type of function could describe this traveler's movement?
2. How would you calculate the rate of travel between 2 and 3 hours?
3. Could the traveler ever return home based on this distance function?
4. If the traveler maintains a constant speed, how could we estimate it from this data?
5. Can the traveler stop moving while still increasing the distance function?

Tip: When analyzing functions, always look for key points like starting values, behavior trends, and maximum/minimum values to better understand the movement or change over time.