2. (5 marks) Consider the function f : R → R defined by Sr if z€ Q S(x) = 10 if reR\Q. (a) (0 marks) Attempt to draw the function. (b) Prove that f is continuous at 0. (c) Let r € Q\ {0}. Prove that f is discontinous at r. Carefully state any results which you use from the course. (Hint: Try the case where r = 1 first; it might give you an idea of how to approach the general case. Partial marks awarded if you only prove it when r = 1.) (d) (Bonus question) Let r € R \ Q. Prove that f is discontinuous at z. [This question is worth 0 marks, but can make up for upto 2 marks lost elsewhere in this assignment.]