The domain of the function is the set of all real numbers. There is no specific interval where the function displays unexpected behavior.

[CODE]:

```python
def f(x):
    if x <= -64:
        return -1.45 * x - 84.97
    elif -64 < x <= 64:
        return 4.84 * x - 307.76
    else:
        return 8.3 * x - 1589.2
```

This piecewise linear approximation captures the observed behavior of the function based on the input-output pairs. However, please note that this is only an approximation and may not accurately represent the actual underlying function implemented by f(x).