Based on the tested values, we can now describe the function.

[DESCRIPTION]:
The function appears to have two different behaviors based on the input (x). For values outside the interval [48, 80], the function maintains an output close to 7.7. However, within the [48, 80] interval, the function's output varies, showing a nonlinear pattern.

[DOMAIN]:
The full domain of the function is [-128, 128], but the interval where the function displays unexpected behavior is [48, 80]. In that interval, the output displays a nonlinear pattern and is not close to 7.7 as it is outside the interval.

[CODE]:
```python
def approx_function(x):
    if 48 <= x <= 80:
        return x / 5
    else:
        return 7.7
```

This approximation assumes that within the interval [48, 80], the function output can be represented by x/5, covering most of the pattern in that interval. And for values outside the interval, the output stays close to 7.7.