The function f(x) appears to have a changing output, based on the input. It can be roughly divided into three intervals. For negative input values, the function seems to show an exponential increase in value as the input value gets closer to 0. For input values around 0, the output remains almost constant. For positive input values, the function seems to show a linear increase in value as x increases.

[DOMAIN]:
- The domain of the function is [-128, 128].
- The interval where the function displays unexpected behavior is around 0. In this interval, the function seems to have a more constant output, compared to the other intervals.
- There are three intervals where the function shows different behavior: negative interval [-128, 0), constant interval [-1, 1], and positive interval (1, 128].

[CODE]:
```python
def approx_function(x):
    if x < 0:
        return 9523 * (2 ** (x / -64))
    elif -1 <= x <= 1:
        return 1.7
    else:
        return x * 282.2 + 1.7

```
This code approximates the behavior of the function based on the observations made from the experiments. It might not be the exact implementation but attempts to closely mimic the tested outputs.