The functional response, describing consumption rate as a function of food abundance, critically links consumer-resource dynamics. Yet, little is known about how its shape affects communities of multiple, dynamically linked species. We theoretically investigated how the functional response of copepods (saturating type 2 vs. sigmoidal type 3, both of which have been observed) mediates bottom-up and top-down influences on the lower oceanic food web as described by five compartments (pentagon web): a shared limiting nutrient, small and large algae, ciliates feeding on small algae, and copepods feeding on ciliates and large algae. We compare system dynamics in response to nutrient enrichment and copepod mortality, the latter being varied first directly and then indirectly through inclusion of planktivores (fish or jellyfish). Regardless of functional response type, when planktivores are absent, equilibrium densities of all members of the even food chain (nutrients-small algae-ciliates-copepods) typically increase with nutrient enrichment whereas large algae decrease. In contrast, and congruent with conventional wisdom, large algae increase with nutrient enrichment when copepods are controlled by planktivores. A type 2 response in copepods strongly destabilizes the pentagon web, whereas stable equilibria are possible when copepods have a type 3 response. High copepod mortality (e.g., caused by increasing planktivore pressure under nutrient enrichment) destabilizes such systems, however. Moreover, because community feedbacks produce a negative correlation between the copepod's alternative prey, type 3 switching behavior is amplified in the pentagon web. This prevents extinctions but can give rise to an alternative state with small algal dominance at high enrichment.