Final answer:
To graph Michael's function, we hypothetically choose two points representing the yards he has left to hike at different times since Justine started hiking. Similarly, two hypothetical points are chosen for Justine's remaining hike distance over time. These points can be plotted on a graph to visually compare their progress.
Step-by-step explanation:
To answer the student's question, we need to analyze the provided information for Michael and Justine's hiking progress and create functions to represent each hiker's remaining distance over time.
Part A: Michael's Function
For Michael's function, we need two points to graph his remaining distance over time. Assuming we have such data, the points might look like this: (Time since Justine started, Yards left). For example, if Michael started two hours before Justine and hiked at a constant rate, after one hour of Justine's hiking, he might have 700 yards left, and after two hours, he might have 400 yards left. The two points here could be (1, 700) and (2, 400).
Part B: Justine's Function
In Justine's function, without explicit information, we create hypothetical points. Since she's been hiking for less time than Michael, her points would likely show a higher remaining distance per the same time intervals. For example, after one hour, she might have 800 yards left, and after two hours, she might have 550 yards left. The points would be (1, 800) and (2, 550).
Part C: Graph Feasibility
To graph the situation, we plot these points on a coordinate system where the x-axis represents time, and the y-axis represents the remaining distance to hike. With just two points for each hiker's function, it's possible to plot a basic linear graph, assuming a constant rate of hiking for simplicity. Plotting these points would allow us to visualize their progress and make comparisons. However, more data points would provide a more accurate portrayal of the hiking progress, and non-linear factors could significantly alter the functions.