To determine whether the situation described by the data table is a function, we need to understand the definition of a function in mathematics:
- A function is a relation where each input (domain) has exactly one output (range).
Let’s analyze the given data. The table shows the height (in meters) of an object at different times (in seconds):
| Seconds (x) | Meters (y) |
|-------------|-------------|
| 0.5 | 28 |
| 1 | 48 |
| 1.5 | 60 |
| 2 | 64 |
| 2.5 | 60 |
| 3 | 48 |
| 3.5 | 28 |
1. Identifying the Inputs and Outputs:
- Inputs (x): {0.5, 1, 1.5, 2, 2.5, 3, 3.5}
- Outputs (y): {28, 48, 60, 64, 60, 48, 28}
2. Checking for Uniqueness of Outputs for Each Input:
- At x = 0.5, y = 28
- At x = 1, y = 48
- At x = 1.5, y = 60
- At x = 2, y = 64
- At x = 2.5, y = 60
- At x = 3, y = 48
- At x = 3.5, y = 28
3. Evaluating if Each Input Corresponds to Exactly One Output:
- Each input value has exactly one output value.
- However, we also need to check if any output value is repeated for different inputs.
Let’s carefully look at the outputs:
- y = 28 appears for x = 0.5 and x = 3.5
- y = 48 appears for x = 1 and x = 3
- y = 60 appears for x = 1.5 and x = 2.5
While evaluating the data, we see that multiple inputs correspond to the same output in several cases.
From these observations, we can state that:
- Even though each input has exactly one output, multiple inputs map to the same output value, indicating that the output values are not unique across different inputs.
Therefore, the correct conclusion for whether this situation describes a function is:
- No, because each input has more than one output. (Referring implicitly to the uniqueness rule from the data analysis)
The situation is not a function because some outputs are repeated for different inputs. Thus the correct answer is:
```
No, because each input has more than one output.
```
