Can Combinations of Monotonically Increasing or Monotonically decreasing functions create a non monotonic function?

Question

I learned that linear combinations of monotonically increasing or decreasing functions are either monotonically increasing or monotonically decreasing, But not monotonic. So are there any kind of combination of monotonic functions that create non monotonic functions like $ \sin (x) $. Or do we always need a non monotonic function to create another non monotonic function.