Say D is not empty.

Consider f(x)=1A) if D is open, then f(D) is open

Consider f(x)=1B) if D is closed, then f(D) is closed

Consider f(x)=x^2 on (0,1).D) if D is not closed, then f(D) is not closed

Heine-Borel Theorem: Compact = Closed + Bounded.E) if D is not compact, then f(D) is not compact

We already talked about closed getting mapped to closed.

You can answer this now.

Consider D=(-oo,+oo) and f(x)=0.F) if D is unbounded, then f(D) is unbounded

Consider f(x)=1/x on (0,1)G) if D is finite, then f(D) is finite

How is that different from unbounded?H) if D is infinite, then f(D) is infinite

It is either an intervalI) if D is an interval, then f(D) is an intervalora single point!