The domain of the function is the set of all real numbers, but the behavior of the function is different in different intervals. 

- In the interval [-128, -8], the function returns a constant value of approximately 3.5. 
- In the interval [-4, 2], the function increases rapidly with increasing values of x. 
- After x = 2, the function reaches a significantly higher value and then becomes constant again for x in the range [4, 128]. 

[CODE]:
```
def f(x):
    if x >= -128 and x <= -8:
        return 3.5
    elif x >= -4 and x < 2:
        return x ** 3 + x ** 2 + x + 4
    else:
        return 11.7
```
Note: This code provides an approximation of the behavior of the function based on the observed values. It may not be an exact representation of the actual implementation.