The function takes an input string and for each lowercase alphabetic character, it adds a constant value to its ASCII representation without affecting the numeric characters. 

[CODE]: 
```python
def approx_function(input_string):
    output_string = ""
    constant = ord('y') - ord('t')  # Calculated based on the response (test1, yeby1)
    
    for char in input_string:
        if char.islower():
            output_string += chr(((ord(char) - ord('a') + constant) % 26) + ord('a'))
        else:
            output_string += char
            
    return output_string
```