The domain of the function is all real numbers. There is no specific interval where the function displays unexpected behavior. However, it is important to note that the function approaches infinity as x approaches 0.

[CODE]:

```python
def f(x):
    if x < 0:
        return -abs(x)
    elif x > 0:
        return abs(x)
    else:
        return float('inf')
```

This code approximates the behavior of the function by checking the sign of the input x and returning the absolute value of x with the appropriate sign. If x is 0, it returns infinity.