Many causal relations can be represented by continuous functions that map inputs to outputs. Can young children learn continuous causal functions and generalize them from observed data to new scenarios? We found that 4- and 5-year-olds can represent continuous functions with different abstract forms. After observing a few input-output pairs, children can accurately infer positive linear and step functions by predicting the outputs of novel input values. They also have emerging knowledge of negative linear and triangular functions. While children do not yet make consistently accurate predictions for these functions, they can distinguish these functions from the positive linear function and show inferential patterns that are consistent with the respective functions. Like adults and older children, preschoolers show an inductive bias towards positive linear functions. Their understanding of negative linear functions--which strongly requires inhibiting this inductive bias--improves with age.