The function seems to be defined for any real number, but the interesting behavior is observed around the interval [-100, 100]. Within this interval, the function displays the quadratic behavior. Outside this interval, the function still exists, but it's hard to determine a clear pattern due to the noise.

[CODE]:
```python
def f(x):
    return -0.02 * (x ** 2) + random.uniform(-10, 10)
```

This is a Python function that approximates the behavior of f(x). It calculates the value of the quadratic function with some added random noise. The coefficient of the quadratic term (-0.02) and the noise range (-10 to 10) may need to be adjusted based on further experimentation and analysis.