Based on the provided data, it seems like the function behaves differently in three intervals: negative values, zero, and positive values. Let's describe the function behavior:

[DESCRIPTION]:
The function f(x) appears to be calculating some linear function for negative and positive input values, while behaving differently for zero. For negative values, the output decreases as the input decreases. For positive values, the output increases as the input increases. At zero, the output is a fixed negative value.

[DOMAIN]:
The function has three distinct domains:

1. Negative domain: x < 0
2. At zero: x = 0
3. Positive domain: x > 0

[CODE]:

```python
def approx_function(x):
    if x < 0:
        return -17.677 * x - 3.7
    elif x == 0:
        return -3.7
    else:
        return 17.552 * x - 3.7
```

Please note that the approximated code may not precisely match the original function but captures the overall behavior observed in the given data.