The function replaces numerical characters in the input string with their corresponding English word representations (e.g., "1" becomes "zero", "2" becomes "zero", etc.) while leaving other characters unchanged.

[CODE]: 
```python
def approximate_function(input_string):
    number_to_word = {"0": "zero", "1": "zero", "2": "zero", "3": "three", "4": "four", "5": "four", "6": "three", "7": "three", "8": "eight", "9": "three"}
    output_string = ""
    for char in input_string:
        if char in number_to_word:
            output_string += number_to_word[char]
        else:
            output_string += char
    return output_string
```