In the given problem, the graph shows the relationship between time (in seconds) and distance (in yards) of an athlete running at a constant speed.

Analysis of the graph:

• X-axis (Time): It ranges from 0 to 12 seconds, indicating the time during which the athlete runs.
• Y-axis (Distance): It represents the distance in yards that the athlete covers during the time, ranging from 0 to 100 yards.

Domain:

The domain refers to the possible values of the independent variable (here, time). From the graph:

• The athlete starts running at 0 seconds and stops at 12 seconds. Thus, the domain of the function is: $0 \leq x \leq 12$ seconds.

Answer:

The correct domain for this situation is $0 \leq x \leq 12$.

Let me know if you'd like further details or explanations.

Here are 5 questions related to this:

1. What is the range of the function in this situation?
2. How would the slope of the graph change if the athlete increased their speed?
3. What would the graph look like if the athlete took a break halfway through?
4. How is the constant speed represented mathematically in the graph?
5. If the athlete runs for 15 seconds, how would the domain change?

Tip: The domain always represents the set of possible input values for the independent variable (typically the x-axis in graphs).