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. (2 points)
Part A:
1) In part 1 of the journey, the bus is gradually increasing its distance from the bus stop.
2) In part 2, the bus has reached a certain distance and is not moving further away from the bus stop. It remains at a constant distance for a period of time.
3) In part 3, the bus starts moving again and gradually increases its distance from the bus stop.
4) In part 4, the bus reaches another point where it remains at a constant distance from the bus stop.
5) In part 5, the bus starts decreasing its distance from the bus stop and eventually reaches the bus stop.
Part B:
- In part 1, 3, and 5, the function is increasing as the bus is moving away from the bus stop.
- In part 2 and 4, the function is constant as the bus is not changing its distance from the bus stop.
Part C:
The graph is non-linear. This is because parts 1, 3, and 5 are smooth curves, indicating that the rate of change of distance with respect to time is not constant. In contrast, a linear graph would show a constant rate of change.