The function takes a string input and performs character substitution on the alphabetic characters while leaving numbers and special characters unchanged.

[CODE]:
```python
def approx_function(input_str):
    subs_dict = {
        'a': 'a', 'b': 'p', 'c': 'l', 'd': 'x',
        'e': 'h', 'f': 'm', 'g': 'q', 'h': 'f',
        'i': 'r', 'j': 'k', 'k': 'g', 'l': 'n',
        'm': 'i', 'n': 'b', 'o': 'u', 'p': 'v',
        'q': 'w', 'r': 'c', 's': 'y', 't': 'e',
        'u': 't', 'v': 's', 'w': 'd', 'x': 'o',
        'y': 'z', 'z': 'j'
    }
    output_str = ''
    for char in input_str:
        if char.isalpha():
            output_str += subs_dict[char.lower()]
        else:
            output_str += char
    return output_str
```
Keep in mind that this is an approximation of the function, as it may not be an exact replication of the original function.