Linearity Rules for Proving Non-Linearity

[shutoutsteve]

Does anyone have a straightforward link to linearity rules? My textbook is not very helpful and my prof never knows what he is talking about :(.
I have a few "prove this is not linear" questions to do
f(x)=(|x1|,|x2|)
f(x)=(1,2)+3x
f(x)=(0,1)

I should know this, but i tend to forget the silly little things.
:(

 

[nealh149]

Basically a function is linear if f(x+y) = f(x) + f(y)