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In the graph, the function describes the relationship between the time \( x \) in seconds and the distance \( y \) in yards, which the athlete covers while running at a constant speed.

### Understanding the Domain:
The domain of a function consists of all the possible input values (in this case, the time \( x \)) for which the function is defined.

- The athlete begins running at \( x = 0 \) seconds and continues running for 12 seconds.
- Therefore, the time values \( x \) range from \( 0 \) to \( 12 \) seconds, inclusive.

### Domain:
The domain of this function is:
\[
0 \leq x \leq 12
\]
This means the function is defined for all values of \( x \) from 0 to 12 seconds.

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Would you like more details or have any questions about this explanation?

Here are five related questions to explore further:
1. What is the range of the function for this situation?
2. How would you calculate the athlete's speed from the graph?
3. What is the slope of the line, and what does it represent in this context?
4. If the athlete continued running for 5 more seconds, how would the graph change?
5. Can you describe how to find the total distance the athlete covered?

**Tip:** The domain represents all the possible values for the independent variable (here, time), while the range represents all possible values for the dependent variable (here, distance).

What is the domain of the function for the athlete's run as described by the graph showing distance as a function of time?

Learn how to find the domain of a linear function representing an athlete's run, where the time in seconds is mapped to distance in yards. This problem covers linear functions and domain concepts, suitable for Grades 6-8 students.

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