To describe the function implemented by f(x), I will run experiments on various inputs and analyze the outputs. I will then provide a description and Python code approximation of the function's behavior.

Experiment 1:
Input: "hello"
Response: "jgnnq"

Experiment 2:
Input: "abc"
Response: "cde"

Experiment 3:
Input: "xyz"
Response: "zab"

From the experiments, it seems that the function implemented by f(x) is shifting each character in the input string by a fixed number of positions in the alphabet. Specifically, it is shifting each character by two positions.

[DESCRIPTION]:
The function f(x) takes a string as input and returns a new string where each character is shifted two positions in the alphabet.

[CODE]:
Here's a Python code approximation of the function:
```python
def shift_characters(string):
    shifted_string = ""
    for char in string:
        if char.isalpha():
            shifted_char = chr((ord(char) - ord('a') + 2) % 26 + ord('a'))
            shifted_string += shifted_char
        else:
            shifted_string += char
    return shifted_string
```

You can call this function with a string as an argument to approximate the behavior of f(x). For example:
```
shifted_result = shift_characters("hello")
print(shifted_result)  # Output: "jgnnq"
```