1. The problem statement, all variables and given/known data t:P_3 -----> P_3 p(x) |---> p(x) + p(2) Determine whether or not this function is linear transformation or not. 2. Relevant equations For a function to be a linear transformation then t(0) = 0 , there are other axioms that must be satisfied, but that is not the problem. 3. The attempt at a solution I don't see how this is a linear transformation, since the zero element of P_3 is where p(x) = 0, and t(p(x)) = t(0) = 0 + p (2) ?? surely? could someone explain why i am totally incorrect please.