Is the elapsed time a function of Brandon’s distance from home? In other words, if you know Brandon’s distance from home, do you know for sure how long it has been since he left?

Question

x
y
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Distance from home (km)
Elapsed Time (min)
The elapsed time
a function of Brandon's distance from home.

Answer 1

To determine if elapsed time is a function of Brandon's distance from home, we need to check whether for any given distance, there is a unique elapsed time associated with it.

Looking at the provided data:

| Distance from home (km) | Elapsed Time (min) | |-------------------------|---------------------| | 0 | 0 | | 10 | 30 | | 20 | 60 | | 30 | 90 | | 40 | 120 | | 50 | 150 | | 60 | 180 | | 70 | 210 | | 80 | 240 | | 90 | 270 | | 100 | 300 |

In this table:

• Each distance corresponds to a unique elapsed time.
• For example, if Brandon is 70 km from home, he has been elapsed 210 minutes since he left.
• If you know any distance (e.g., 50 km), you can determine the exact elapsed time (150 minutes) without ambiguity.

Since for every distance from home, there is a unique elapsed time, we can conclude that the elapsed time is indeed a function of Brandon's distance from home.