We present new means for performing static program analysis on serverless programs. We propose a new type of call graph that captures the stateless, event-driven nature of such programs and describe a method for constructing these new extended service call graphs. Next, we survey applications of program analysis that can leverage our extended service call graphs to answer questions about code that executes on a serverless platform. We present findings on the applicability of our techniques to real open source serverless programs. Finally, we close with several open questions about how to best incorporate static analysis in problem solving for developing serverless applications.