1.6.22 Fields, Groups, Rings

Problem: Two groups and a mapping between them are given. Is the given mapping a homomorphism, epimorphism, monomorphism, isomorphism? \[ \begin{array}{l} \left(Z_{3},+\right),\left(Z_{9},+\right), \\ f(\overline{0})=\overline{0}, \quad f(\overline{1})=\overline{3}, \quad f(\overline{2})=\overline{6} . \end{array} \]