1. f has a discontinuity in every rational number, but is continous everywhere else, and
2. f is monotonic: x<y → f(x)<f(y)

Note: Textbooks frequently present examples of functions that meet only the first condition; requiring monotonicity makes for a slightly more challenging problem.

My problem is

Since every epsilon neighborhood of an irrational number contains a rational number, how can the function be continuous at the irrational numbers.