Final answer:
To graph Jacob's function of laps versus distance, points corresponding to the number of laps and respective distances would be plotted on a graph with 'Number of Laps' on the x-axis and 'Distance (miles)' on the y-axis. The domain would involve the laps numbers {2, 3, 4, 5, 6, 7, 8}, and the range would include the distances {0.5, 0.75, 1, 1.25, 1.5, 1.75, 2}.
Step-by-step explanation:
Jacob has been recording the number of laps and the distance he walks on a track each day. To graph the function based on his records and to describe the domain and range, we need to interpret the given set of points as input-output pairs where the first value of each pair is the number of laps (input), and the second value is the distance in miles (output).
Graphing the Function
To plot the graph, we would label the x-axis as 'Number of Laps' and the y-axis as 'Distance (miles)'. The given points are (3, 0.75), (6, 1.5), (5, 1.25), (2, 0.5), (7, 1.75), (8, 2), and (4, 1). These points would be plotted on the Cartesian plane corresponding to these axes.
Domain and Range
The domain of the function represents all the possible input values, which in this case is the set of lap counts Jacob recorded: {2, 3, 4, 5, 6, 7, 8}. The range is the set of all possible output values, or the distances that correspond with the lap counts: {0.5, 0.75, 1, 1.25, 1.5, 1.75, 2}.