Final answer:
The domain and range of the relation are both sets of non-negative real numbers, interpreting the relation as a function where each hour corresponds to a specific distance traveled. The graph of this function would show the distance on the y-axis against the time on the x-axis, where the slope represents the speed.
Step-by-step explanation:
The relation represents time driven in hours (the independent variable) and the number of miles traveled at the end of each hour (the dependent variable). To determine the domain and range of this relation, consider that the domain is the set of all possible input values, which would be the time in hours. Since one does not typically drive a negative amount of time, the domain could be all non-negative real numbers. The range would be the total number of miles traveled, which also cannot be negative, representing the set of non-negative real numbers.
Interpreting this in context, as time increases, the miles traveled would also increase. This scenario is indeed a function, as each hour of driving corresponds to exactly one particular distance traveled. There is a unique output (miles traveled) for every input (time driven). Analyzing such a relationship is crucial, especially when considering economic models or understanding mathematical functions as they apply to various aspects like physics, where time and displacement, position, or acceleration are typically graphed as functions of time, depicting how these quantities depend on time.
In the example given, if we were to graph a line for the relationship between time and miles driven, the slope of that line would represent the speed (rate at which the vehicle is traveling) and the y-intercept would typically be the starting point for the miles driven, which in a real-world scenario might be zero, indicating the trip started at that point.