Question

1. is distance a function of time? explain your thinking.
2. is time a function of distance? explain your thinking.

(chart: time (seconds) | distance (meters)
13.8 | 100
15.9 | 100
16.3 | 100
17.1 | 100
18.2 | 100
distance (meters) | time (seconds)
100 | 13.8
100 | 15.9
100 | 16.3
100 | 17.1
100 | 18.2)

Explanation:

For Question 2:

A function requires each input to have exactly one output. For distance as a function of time, each time value (input) maps to only one distance value (output, 100 meters here). So this meets the definition of a function.

For Question 3:

A function requires each input to have exactly one output. For time as a function of distance, the single distance input (100 meters) maps to multiple different time values (13.8, 15.9, 16.3, 17.1, 18.2 seconds). This violates the function definition.

Answer:

1. Yes, distance is a function of time. Each unique time value corresponds to exactly one distance value (100 meters), satisfying the function requirement that every input has one output.
2. No, time is not a function of distance. The single distance value (100 meters) corresponds to multiple different time values, which violates the rule that a function must have one unique output per input.