The graph represents the journey of a bus from the bus stop to different locations:
The title for the graph is Bus Journey. The label on the y-axis is Distance in miles, and the label on the x-axis is Time in hours. The graph shows 5 parts. The part labeled 1 is a smooth curve going up from the origin. The part labeled 2 is a straight horizontal line. The part labeled 3 is a smooth curve going up. The part labeled 4 is a straight horizontal line. The part labeled 5 is a smooth curve going down that touches the x-axis.
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)
Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)
Part C: Is the graph linear or non-linear? Explain your answer.
Part A:
1. In part 1 of the journey, the bus is gradually increasing its distance from the bus stop over time. It is moving forward steadily and smoothly.
2. In part 2 of the journey, the bus has reached a certain distance from the bus stop and remains at that distance for a period of time. It is not moving further away but maintaining a constant distance from the bus stop.
3. In part 3 of the journey, the bus starts moving forward again and continues to increase its distance from the bus stop over time. Similar to part 1, it is moving forward steadily and smoothly.
4. In part 4 of the journey, the bus once again reaches a certain distance from the bus stop and remains at that distance for a period of time. It is not moving further away but maintaining a constant distance from the bus stop.
5. In part 5 of the journey, the bus starts moving back towards the bus stop, gradually decreasing its distance over time. It is moving backwards steadily and smoothly until it reaches the bus stop again.
Part B:
- The function is increasing in parts 1 and 3, as the bus is moving forward and increasing its distance from the bus stop.
- The function is constant in parts 2 and 4, as the bus maintains a constant distance from the bus stop.
- The function is decreasing in part 5, as the bus is moving backwards towards the bus stop and decreasing its distance.
Part C:
The graph is non-linear. This can be seen because the curves in parts 1, 3, and 5 indicate a changing rate of distance over time. In a linear graph, the line connecting the points would be a straight line, while in this graph, the curves indicate a non-linear relationship between distance and time.