Let $f:C\to C'$ be a functor, and let $A$ be a locally presentable, complete, and cocomplete category. Then according to the paper I'm reading, the pullback functor, $f^*:A^{C'}\to A^C$ (given by precomposition with $f$), admits left and right adjoints $f_!$ and $f_*$. It's clear that the proof of this fact follows from the adjoint functor theorem, so it suffices to show that $f^*$ is continuous and cocontinuous.

However, it's not clear to me how to show this fact.

Question:

Using the notation above, why is $f^*$ continuous and cocontinuous?

Sorry if this ends up being too easy.