In reply to jwdmotorsports:
Is the frame steel or aluminum? Are the plastics original? What's the headlight configuration? Tire sizes? Yamaha put the Genesis name on a bunch of bikes from middle 80's to the early 90's. If you've got an aluminum deltabox (should have a sticker saying this on the frame) frame and a trapezoidal headlight you've got an FZR1000 (this is what I'm usually riding these days). If it's a steel deltabox frame, has twin round headlights, and a tire size around 130/70/18. If it's an aluminum deltabox frame with twin round headlights it's probably an FZR400. The Genesis name was also applied to the FZ750 as well. That one had a steel perimeter frame and twin headlights.
You might be able to find the engine size by removing the side fairings and looking around the the cylinders. Japanese manufacturers typically cast numbers denoting the size into them.
This is about the best FZR specific site I've come across - www.fzrarchive.com