We introduce a set of nine challenge tasks that test for the understanding of function words. These tasks are created by structurally mutating sentences from existing datasets to target the comprehension of specific types of function words (e.g., prepositions, wh-words). Using these probing tasks, we explore the effects of various pretraining objectives for sentence encoders (e.g., language modeling, CCG supertagging and natural language inference (NLI)) on the learned representations. Our results show that pretraining on language modeling performs the best on average across our probing tasks, supporting its widespread use for pretraining state-of-the-art NLP models, and CCG supertagging and NLI pretraining perform comparably. Overall, no pretraining objective dominates across the board, and our function word probing tasks highlight several intuitive differences between pretraining objectives, e.g., that NLI helps the comprehension of negation.