Question

Could you still use your sewing machine if your feed dogs were not functioning? Why or why not?

Answer 1

Yes, you could do free motion embroidery, quilting or darning on it, but not standard seaming. 

Usually feed dogs don't work because they're dropped (look for a switch), or they're fouled with a thread jam (remove the needle plate (=throat plate) and clean thoroughly), or they haven't been lubricated in half of forever (take it in for a pro cleaning or try to DIY with a small drop of sewing machine oil.)