1. The graph represents a function because the graph passes the vertical line test. This means that no one x-value has two y-values. If we run a vertical line throughout the graph, the line will only intersect the graph once.
2. The domain of the graph in interval notation is [0, 17] because the possible x-values shown in the graph are only from 0-17 units of time.
3. The range of the graph in interval notation is [0, 10] because the possible y-values shown in the graph are only from 0-10 units of distance.
4. The maximum distance is 10 units of distance.
5. The minimum distance is 0 units of distance.
6. The intervals in which the graph is increasing are from time = 0 to 5, 10 to 12, and 14 to 15. In interval notation, it is (0, 5) ⋃ (10, 12) ⋃ (14, 15).
This means that during these intervals, the speed is accelerating or an object is moving fast. The slope is positive.
7. The intervals in which the graph is decreasing are from time = 7 to 10, 12 to 14, and 15 to 17. In interval notation, it is (7, 10) ⋃ (12, 14) ⋃ (15, 17).
This means that during these intervals, the speed is decelerating or the object is slowing down. The slope is also negative.
8. Lastly, the interval in which the graph is constant is from time = 5 to time = 7. In interval notation, it is (5, 7).
This means that the speed is constant and is able to cover a constant distance which is 5 units of distance per unit of time from time = 5 to 7.