Question

What is an appropriate domain and range for the problem situation in the context of Tyburn's drive from El Paso to Orange, where he is driving at an average rate of 60 mph over a distance of 834 miles? A) Domain: [0, 834] miles, Range: [0, [infinity]) hours B) Domain: [0, [infinity]) hours, Range: [0, 834] miles C) Domain: (-[infinity], [infinity]) hours, Range: (-[infinity], [infinity]) miles D) Domain: [0, 834] miles, Range: [0, 60] mph

Answer 1

The problem involves a drive of a fixed distance, so the domain is limited to the time needed to cover that distance. The range is the limited distance covered. The best answer from the choices is Domain: [0, infinity) hours, Range: [0, 834] miles.

Step-by-step explanation:

In a problem involving distance, rate, and time, the domain typically represents the time duration of the scenario, while the range signifies the associated distance covered. In the context of Tyburn's drive from El Paso to Orange for a fixed distance of 834 miles at a rate of 60 mph, the domain would be the amount of time traveled, and that cannot exceed the time it takes to drive 834 miles at 60 mph. Therefore, the domain is limited from 0 to a maximum of 834/60, approximately 13.9 hours. The range is the distance Tyburn covers, which starts at 0 and ends when he reaches his destination, therefore it is [0, 834] miles. So, the appropriate answer is Domain: [0, 834/60] hours, Range: [0, 834] miles. None of the provided options are exactly correct, but option B) Domain: [0, [infinity]) hours, Range: [0, 834] miles is the most similar one.

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