Answer:
A horizontal line segment from (0, 0) to (t1, d1).
A descending line segment from (t1, d1) to (t1 + t2, d1 - d2).
An ascending line segment from (t1 + t2, d1 - d2) to (t1 + t2 + t3, d1 - d2 + d3).
Step-by-step explanation:
To graph the distance between George and his home as a function of time, we need to consider the different segments of his journey.
Let's assume that George's home is at the origin (0,0) on the graph.
Segment 1: Bicycling from home to the point of the flat tire.
During this segment, the distance remains constant as George has not covered any additional distance. Let's say this distance is d1.
Segment 2: Backtracking to the service station.
During this segment, George is moving in the opposite direction, so the distance decreases. Let's say he backtracks a distance of d2.
Segment 3: Bicycling from the service station to school.
During this segment, the distance increases as George moves towards his school. Let's say he covers a distance of d3.
To graph these segments, we need to determine the relationship between time and distance for each segment. We'll assume that George travels at a constant speed.
Segment 1: Let t1 represent the time taken for George to get the flat tire.
Distance during segment 1: d1 = speed * t1
Segment 2: Let t2 represent the time taken for George to backtrack to the service station.
Distance during segment 2: d2 = speed * t2
Segment 3: Let t3 represent the time taken for George to reach school from the service station.
Distance during segment 3: d3 = speed * t3
To graph the distance, we plot the points (t, d), where t represents the time elapsed and d represents the distance from George's home.
The graph will have three segments:
1. A horizontal line segment from (0, 0) to (t1, d1).
2. A descending line segment from (t1, d1) to (t1 + t2, d1 - d2).
3. An ascending line segment from (t1 + t2, d1 - d2) to (t1 + t2 + t3, d1 - d2 + d3).
The graph represents the distance between George and his home as he travels from home to school, considering the flat tire, backtracking, and the remaining journey to school.