To determine if a relation represents a function, we need to check if every input (in this case, time in seconds) corresponds to exactly one output (height in meters). In other words, for the relation to be a function, each time value must be unique and map to only one height value.
Let's examine the given data set:
| Time (in seconds) | Height (in meters) |
|--------------------|--------------------|
| 0 | 20 |
| 1 | 19.2 |
| 2 | 16.8 |
| 2.5 | 15 |
| 3 | 12.8 |
| 4 | 7.2 |
| 5 | 0 |
We will go through each time value to see if it appears more than once:
- Time 0: Appears once.
- Time 1: Appears once.
- Time 2: Appears once.
- Time 2.5: Appears once.
- Time 3: Appears once.
- Time 4: Appears once.
- Time 5: Appears once.
Each time value is unique and maps to exactly one height value. Since there are no repeated time values, this relation meets the criteria of a function.
Therefore, the given relation is a function.
Answer: True
