Let f(x) = 0 if x is irrational and let f (x) = 1/q if x is

Question:

Let f(x) = 0 if x is irrational and let f (x) = 1/q if x is the rational number p/ q in reduced form (q > 0).
(a) Sketch (as best you can) the graph off on (0, 1).
(b) Show that f is continuous at each irrational number in (0, 1), but is discontinuous at each rational number in (0, 1).