What is the range of the function for this situation?
Understand the Problem
The question is asking for the range of a linear function that represents the distance in yards run by an athlete over a time of 12 seconds. The answer should reflect the maximum distance that corresponds to that time on the given graph.
Answer
All real numbers greater than or equal to $0$ and less than or equal to $12$.
Answer for screen readers
The range of the function is: all real numbers greater than or equal to $0$ and less than or equal to $12$.
Steps to Solve
- Identify the context of the problem
The problem presents a scenario where an athlete runs for 12 seconds. We need to find the range of the function that represents the distance (in yards) run over time (in seconds).
- Determine the endpoints for time and distance
According to the graph, the time $x$ ranges from $0$ seconds to $12$ seconds. We look for the corresponding distance $y$ values at these endpoints.
- Analyze the distance at the endpoint
From the graph, we observe that the maximum distance when $x = 12$ seconds is $y = 12$ yards. Thus, the distance varies from $0$ to $12$ yards.
- Define the range of the function
The range reflects the possible output values of the function for $x$ between $0$ and $12$ seconds. The outputs correspond to the distances run, which are in the interval from $0$ to $12$ yards.
- Summarize the findings
The range of the function is therefore all real numbers greater than or equal to $0$ and less than or equal to $12$.
The range of the function is: all real numbers greater than or equal to $0$ and less than or equal to $12$.
More Information
This means the athlete could run anywhere from $0$ yards (not moving) to $12$ yards during the 12 seconds. This analysis helps understand how distance relates to time in linear motion.
Tips
- Misinterpreting the graph could lead to incorrect values for the distance.
- Forgetting to consider both the lower and upper bounds of the range might affect the final answer.