Based on the input-output pairs we obtained:
- When the input x is negative, the output seems to be a negative value as well, with the magnitude increasing as x gets closer to 0.
- When the input x is positive, the output appears to be a positive value, with the magnitude increasing as x gets further away from 0.
- The output values seem to follow a quadratic-like pattern, increasing as x moves away from 0 in both positive and negative directions.

From these observations, we can describe the function implemented by f(x) as follows:

[DESCRIPTION]:
The function f(x) takes a numerical input x and returns a value that is proportional to x^2 and has the same sign as x. It exhibits a quadratic-like behavior, with the magnitude of the output increasing as the absolute value of x increases.

[DOMAIN]:
The domain of the function f(x) is the set of all numerical values. There is no specific interval where the function displays unexpected behavior. However, the behavior of the function changes sign at x = 0, from negative for negative x values to positive for positive x values.

[CODE]:
Based on the observations, we can approximate the behavior of the function with the following Python code:

```python
def f(x):
    return x**2 * (-1 if x < 0 else 1)
```

This code first computes the square of the input x and then multiplies it by -1 or 1 depending on the sign of x. This code approximates the behavior of the function f(x) described above.