The domain of the function is the set of all numerical inputs. However, there is an interval where the function displays unexpected behavior, which is from -128 to 0. In this interval, the function consistently outputs a negative value close to -7.3. The function behaves differently before and after this interval.

[CODE]:
```python
def f(x):
    if x <= 0:
        return -7.3
    else:
        return x * 0.06171875 + 7.9
```

This code is an approximation of the behavior observed from the experiments. It checks if the input, `x`, is less than or equal to 0. If so, it returns a constant value of -7.3. Otherwise, it applies a linear transformation to the input and adds a constant value of 7.9 to get the output.

Please note that the provided description and approximation are based on the observed behavior of the function from the limited experiments. For a more accurate analysis, additional experiments and data points may be needed.