Hi. I made a website at yahoo small business host account. I think I also purchased my domain name through them. My website is about industrial equipment that I manufacture. My website is the first result when doing a search at yahoo pertaining to this sort of equipment. I dont want to lose that. My question is will I lose my ranking in the search results if I host my website at bravenet as opposed to yahoo small business?

Hello,
if you change domain names in addition to the change of host, you need to make a 301 redirect from your old domain to your new domain.

If you have only changed your hosting, there is no need to worry.