The function has a domain of all real numbers. The unexpected behavior is observed for positive input values greater than 0.

[CODE]:
```python
def f(x):
    if x > 0:
        return -10.9
    else:
        return -1.9
```
The code above approximates the behavior of the function. It uses an if-else statement to check if the input value is greater than 0. If it is, it returns -10.9. Otherwise, it returns -1.9.