Lots of people will disagree with me, but I think if a big game animal is too far away to see clearly with a 3x9 scope at 9 power, you should not be shooting at it. With a smaller scope your rifle will balance better, and you will not be tempted to take shots that are too long, or in poor light. When I gave my son a big game rifle, it had a fixed 3x scope on it, and I told him that if he shot at an animal more than 200 yards away I'd take it back.
This is definitely not the prevailing attitude anymore, what with people ambushing game from fixed stands and a steady rest, so you'll probably want to ignore my advice. For myself, I had to give up hunting, since I like to sit or sneak along on the ground, and here in the East I'm definitely afraid I'll get shot.