Who are you training with Random? Alt failure in an R44 is an emergency you could face (battery failure without the red Alt light fIrst is less likely) so you need to know how to address it before being qualified.
You can continue in flight without the Alt but you have limited time before loss of key instruments, transponder, radios, etc
Not a big deal but note, the AFM says Land as soon as Practicable, so you have time to divert and not panic.
Please talk to your instructor and get them to explain what to do for this key emergency.
H-R 01