The correct answer is Option A. The for file in "$@"; do ...; done loop correctly iterates over the list of arguments passed to the script. For each iteration, if [ -e "$file" ]; then checks if the current file exists with -e (file exists test operator) and the following echo "File $file exists" statement prints the appropriate message. Double-quoted $file prevents issues with filenames containing spaces or special characters.

Option B is incorrect because it checks if a string literal '$file exists' rather than checking if each file exists. Option C is incorrect as it checks for the variable $file_name which is not defined in the context and also uses incorrect syntax for testing file existence. Option D is incorrect because it uses << redirection operator, which is used to redirect input from a here document and is not a proper way to check for the existence of files.