How far it goes depends on several variables, probably the most significant of which are the barrel length and the load you're shooting. How far it will go is not so important as what it has left to do the job when it gets there. Shot placement is just as important as ballistics.

If I were hunting elk with a .44 mag, I'd shoot the heaviest bullet I could find, something in a jacketed soft point. With proper shot placement, I think a 240 gr. JSP would do the job out to a hundred yards.

Re: scopes, iron sights and 'knowing the gun,' you have a responsibility to the game to be able to hit what you're shooting at. No one wants wounded game running around out there. There's a deer around my home right now with a front foreleg shot off. She's making it, but it's not a pretty picture. Choose your rifle and load and practice, practice, practice. It doesn't matter what the effective range of the gun is, what matters is the effective range of the shooter. The range at which you can put all of your shots in a 10-12" circle is your effective range.

I was recently telling a friend of the deer I harvested with a .357, and how it was 30 yards out but I didn't shoot. He said 'that's handgun range.' My immediate reply was 'not for me.' Because I had practiced and knew my effective range.

Have fun and good luck.