(a) Show that the sample variance is unchanged if a constantcis added to or subtracted from each value in the sample.

(b)Show that the sample variance becomes times its original value if each observation in the sample is multiplied by c.

This was something our professor gave us to do. I showed both by using problem examples from our textbook, but he said that it would be wise to be able to give a general proof for each, should it come up on our exam. I've never really done any proofs so I'm at a bit of a loss as where to start and whatnot. I'll be trying to figure this out but any help would definitely be appreciated.