Gene regulation networks contain recurring circuit patterns called network motifs. One of the most common network motif is the incoherent type 1 feed-forward loop (I1-FFL), in which an activator controls both gene and repressor of that gene. This motif was shown to act as a pulse generator and response accelerator of gene expression. Here we consider an additional function of this motif: the I1-FFL can generate a non-monotonic dependence of gene expression on the input signal. Here, we study this experimentally in the galactose system of Escherichia coli, which is regulated by an I1-FFL. The promoter activity of two of the gal operons, galETK and galP, peaks at intermediate levels of the signal cAMP. We find that mutants in which the I1-FFL is disrupted lose this non-monotonic behavior, and instead display monotonic input functions. Theoretical analysis suggests that non-monotonic input functions can be achieved for a wide range of parameters by the I1-FFL. The models also suggest regimes where a monotonic input-function can occur, as observed in the mglBAC operon regulated by the same I1-FFL. The present study thus experimentally demonstrates how upstream circuitry can affect gene input functions and how an I1-FFL functions within its natural context in the cell.