Big O notation focuses on the worst case, which is O(n) for the simple search. It's a guarantee that the simple search will never be slower than O(n) time. In a code where the worst scenario is go thought all the elements the notation is O(n)

def print_items(n):
    for i in range(n):
        print(i)

print_items(10)

The time complexity increases proportionally to the given input.