The domain of the function seems to be the entire numeric range, including negative and positive values. However, there seems to be a significant change in behavior around the input value of 0.

In the given experiment, the function becomes negative for negative input values and approaches a significantly large negative value as the input approaches 0. For positive input values, the function remains negative but approaches a smaller negative value as the input approaches 0. It then starts to increase again for positive input values.

[CODE]:

```python
import math

def f(x):
    if x < 0:
        return -1.7  # Constant value observed for negative input values
    elif x == 0:
        return -511.3  # Constant value observed for input value of 0
    else:
        return -10.9  # Constant value observed for positive input values
```

Please note that this is just an approximation of the behavior based on the limited experiments conducted. Further experiments with a larger range of input values would be necessary to provide a more accurate description of the function.