Transcriptional regulator involved in different processes such as glucose metabolism, aerobic glycolysis and autophagy (PubMed:25402684, PubMed:29861159, PubMed:30700909). Recognizes and binds the forkhead DNA sequence motif (5'-GTAAACA-3') and can both act as a transcription activator or repressor, depending on the context (PubMed:25402684, PubMed:29861159, PubMed:30700909). Together with FOXK1, acts as a key regulator of metabolic reprogramming towards aerobic glycolysis, a process in which glucose is converted to lactate in the presence of oxygen (PubMed:30700909). Acts by promoting expression of enzymes for glycolysis (such as hexokinase-2 (HK2), phosphofructokinase, pyruvate kinase (PKLR) and lactate dehydrogenase), while suppressing further oxidation of pyruvate in the mitochondria by up-regulating pyruvate dehydrogenase kinases PDK1 and PDK4 (PubMed:30700909). Probably plays a role in gluconeogenesis during overnight fasting, when lactate from white adipose tissue and muscle is the main substrate (PubMed:30700909). Together with FOXK1, acts as a negative regulator of autophagy in skeletal muscle: in response to starvation, enters the nucleus, binds the promoters of autophagy genes and represses their expression, preventing proteolysis of skeletal muscle proteins (PubMed:25402684). In addition to the 5'-GTAAACA-3' DNA motif, also binds the 5'-TGANTCA-3' palindromic DNA motif, and co-associates with JUN/AP-1 to activate transcription (By similarity). Also able to bind to a minimal DNA heteroduplex containing a G/T-mismatch with 5'-TRT[G/T]NB-3' sequence (By similarity). Binds to NFAT-like motifs (purine-rich) in the IL2 promoter (By similarity). Positively regulates WNT/beta-catenin signaling by translocating DVL proteins into the nucleus (By similarity). Component of SIN3A-, but not SIN3B-, containing multiprotein complexes (PubMed:25402684). Interacts with DVL1, DVL2 (when phosphorylated) and DVL3; the interaction induces DVL2 nuclear translocation (By similarity). Interacts with SUDS3 (By similarity). Interacts with BAP1 (when phosphorylated); leading to recruit the PR-DUB complex and repress FOXK2 target genes (By similarity). Expressed in a wide range of adult brain regions, namely the piriform cortex, the major islands of Calleja and cells lining the lateral ventricles, the bed nucleus of stria terminalis, the paraventricular thalamic nucleus, habenula and all structures of the hippocampus. Also present in the hypothalamus, cerebral cortex and in the Purkinje cell layer in the cerebellum. Additionally expressed in dopamine neurons of the substantia and more sparsely in the ventral tegmental area. At 12.5 dpc, expressed ubiquitously in the developing central nervous system. This pattern persists at 14.5 dpc and 16.5 dpc, with expression levels varying. The C-terminal part of the DNA-binding domain may contribute to DNA recognition specificity. Hyperphosphorylated during mitosis by CDK1 and, to a lower extent, CDK2. Phosphorylation at Ser-364 and Ser-419 affects stability by promoting degradation.