I am doing the following problem for practice to understand linear transformations.
Consider the linear transformation $T:P_2 \rightarrow P_2$ defined by: $$ T(p(x)) = p(x+1) $$ Where $P_2$ is the vector space of polynomials of at most degree 2. Determine whether T is injective, surjective, or bijective.
The problem I am having trouble on how to start this. Just from using my intuition I would say that the $T$ is bijective partially because it is going from one vector space to the same vector space. But I am unsure of how to show this. If anyone can help me I would greatly appreciate it.