Let f->R be continuous. For each of the following, prove or give a counter example:

a) If D is open, then f(D) is open

b) if D is closed, then f(D) is closed

c) If D is unbounded, then f(D) is unbounded

d) If D is finite, then f(D) is finite

e) If D is infinite, then f(d) is infinite.

I need to know counter examples for a,b,c, and e and how to prove d is true.