linear algebra question

For a fixed constant ce R, define a function Ec : P -> R by Ec(p) = p(c). (This is called the "evaluation at c" function.) (a) (3 points) Show that Ec is a linear transformation. (b) (2 points) What is the dimension of ker(Ec)? (c) (1 point) Polynomials in ker(Ec) all have graphs with a specific geometric property. What is this property