The domain of the function is from -128 to 128. The interval where the function behaves unexpectedly is between -2 and 2.

[CODE]:

```python
def f(x):
    if x < -2 or x > 2:
        return 1.0
    else:
        # Calculate the function's behavior within the interval [-2, 2]
        # Insert your own code here to approximate the specific behavior within the interval
        return f_within_interval(x)

def f_within_interval(x):
    # Approximate the behavior within the interval [-2, 2]
    # You can use additional experiments or analysis to determine the behavior within this interval
    # Insert your own code here to approximate the specific behavior within the interval
    
    # As an example, let's assume the behavior within the interval is a quadratic function
    return x**2

# You can call the function on any value within the domain
print(f(1))
```

Please note that the code snippet above is just an example and the actual behavior within the interval [-2, 2] may be different. You can refine and further analyze the behavior in that interval by running additional experiments or using more advanced techniques.