The domain of the function is the entire range between -128 and 128. However, there is an interval where the function displays unexpected behavior. This interval is around x = 16 to x = 32, where the function reaches a peak and starts to decrease significantly. Additionally, the function also exhibits a sharp decrease around x = -32.

[CODE]:
```python
def f(x):
    if x < -32:
        return -3.272328623364942
    elif x >= -32 and x < 16:
        return x + 3
    elif x >= 16 and x <= 32:
        return 4 + 0.2 * (x - 16)
    else:
        return -0.699845037530283
```

Please note that the code approximation is just an approximation based on the observations from the experiments. The actual implementation of the function may differ, but this should give a good representation of its behavior.