The function returns the input string with occasional character substitutions.

[CODE]: 
```python
def approximate_function(input_string):
    # Based on the observed behavior, the code below is an approximation and might not cover all cases.
    change_dict = {'u': 'k', 'm': 'k'}
    
    output_string = ''.join([change_dict.get(char, char) for char in input_string])
    
    return output_string
```

Let's test the approximation function.

COMMAND: PYTHON(./temp/function.py "The quick brown fox" "jumps over the lazy" "d0g and grabs the b0ne" "A1b2C3d4E5f6G7H" "Mix of *symbols* and text!")