The domain of the function is the set of real numbers (-∞, +∞). However, there is an interval where the function displays unexpected behavior. This interval is around x = 0. For input values close to 0, the function outputs negative values that are significantly smaller in magnitude compared to the outputs for input values further away from 0.

[CODE]:
Based on the observations, one possible approximation of the function could be a quadratic function. Here's an example of Python code that approximates the behavior of the function:

```python
def f(x):
    return -0.01 * x**2
```

Please note that this is just an approximation based on the observed behavior and may not perfectly capture the exact function implemented by f(x).