The domain of the function is the interval [-128, 128]. Within this interval, there is an interval where the function displays unexpected behavior. This interval is approximately [-30, -20]. Outside this interval, the function behaves like a linear function.

[CODE]:
To approximate the behavior of the function, we can use the following Python code:

```python
import math

def f(x):
    if -30 <= x < -20:
        return math.sin(x)
    else:
        return x * 2
```

This code defines a function f(x) that approximates the behavior of the original function. It uses the math.sin() function to handle the unexpected behavior within the interval [-30, -20]. Outside this interval, it simply multiplies the input x by 2.

Please note that this approximation is based on the experiments conducted and may not perfectly represent the original function f(x) implemented in the script.