= Solution
Without added <HNF1β>, both <TCF transcription factor> isoforms increase reporter output over the empty-vector baseline, with TCF-short giving the larger increase. Adding <HNF1β> leaves TCF-short output near $3800$–$4000$ arbitrary units, but reduces TCF-long-associated output from roughly $3200$ to $300$–$400$, approximately a tenfold reduction. The empty-vector baseline falls only modestly. \b[<HNF1β> therefore supports strong isoform-selective repression associated with TCF-long, while TCF-short remains activating in this assay.]
This pattern is consistent with recruitment of a <transcription corepressor> through the long-specific interaction motif. To test that mechanism directly, mutate the motif while preserving expression and DNA binding, rescue with the intact version, mutate the promoter binding sites, and measure the abundance and localization of both factors. Reporter output alone does not establish the molecular contact or the same quantitative effect at the endogenous <GLP-1 receptor> locus. The question prose and figure caption name different host <cell lines>, so cell-line-specific mechanistic conclusions require clarification of that source inconsistency.
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