The domain of the function is the set of all numerical values. There is no interval within the domain where the function displays unexpected behavior. The function behaves consistently by returning 1 for negative inputs and -1 for positive inputs.

[CODE]:

```python
def f(x):
    if x < 0:
        return 1
    else:
        return -1
```

This code approximates the behavior of the function by using an if-else statement to check whether the input value is less than 0. If it is, the function returns 1; otherwise, it returns -1.