Question

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?
x
y
0
10
20
30
40
50
60
70
80
90
100
0
30
60
90
120
150
180
210
240
270
300
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**.