Based on the results for integer values between -50 and 50, we can observe the following:
- For x ≤ -6, f(x) = 9.7
- For -6 < x ≤ 0, f(x) decreases non-linearly, and there is some noise.
- For 0 < x ≤ 50, f(x) = 0.7

To describe the function:

[DESCRIPTION]:
f(x) returns a value of 9.7 for x less than or equal to -6, decreases non-linearly with some noise for x between -6 and 0, and returns a value of 0.7 for x greater than 0.

[DOMAIN]:
The unexpected behavior interval is when -6 < x ≤ 0. This is when the function's output decreases non-linearly and has some noise.

[CODE]:
```python
def approximate_function(x):
    if x <= -6:
        return 9.7
    elif -6 < x <= 0:
        return 9.7 - (9.7 - 0.7) * ((x + 6) / 6)**2  # Assuming a simple polynomial decrease, this can be further improved.
    else:
        return 0.7
```

Please note that the approximation function may not cover every intricate detail of the real function, and can be further refined for the interval between -6 and 0.