I've been having trouble in my Advanced Calculus class and I'm not sure how to prove this. I was wondering if someone here could help.

Let D be a subset of R^n and f mapping from D to R^m be continuous.

a.) Prove that if D is connected, then the range of f is connected.

b.) Prove that if D is compact, then the range of f is compact.

Thanks in advance (and sorry I don't know how to get the math symbols on this site to make it clearer.)