Histone lysine demethylase with selectivity for mono- and dimethylated residues. It plays an essential role in cell cycle progression and rDNA transcription (PubMed:19843542, PubMed:20531378, PubMed:20548336, PubMed:20622854). Demethylates mono- and dimethylated histone H3 'Lys-9' residue (H3K9Me1 and H3K9Me2) and monomethylated histone H4 'Lys-20' residue (H4K20Me1). Acts as a transcription activator as H3K9Me1, H3K9Me2, H3K27Me2 and H4K20Me1 are epigenetic repressive marks (PubMed:20101266, PubMed:20208542, PubMed:20346720, PubMed:20622853, PubMed:20622854). Displays a very low intrinsic activity toward dimethylated H3 'Lys-27' (H3K27Me2) (PubMed:20346720). May also have weak activity toward dimethylated H3 'Lys-36' (H3K36Me2), however, the relevance of this result remains unsure in vivo (PubMed:19843542, PubMed:20023638, PubMed:20346720). Involved in cell cycle progression by being required to control G1-S transition (PubMed:20622854). Acts as a coactivator of rDNA transcription, by activating polymerase I (pol I) mediated transcription of rRNA genes (PubMed:20531378). Specifically binds trimethylated 'Lys-4' of histone H3 (H3K4me3), affecting histone demethylase specificity: has weak activity toward H3K9Me2 in absence of H3K4me3, while it has high activity toward H3K9me2 when binding H3K4me3 (PubMed:20023638, PubMed:20346720, PubMed:20421419). Positively modulates transcription of histone demethylase KDM5C, acting synergistically with transcription factor ARX; synergy may be related to enrichment of histone H3K4me3 in regulatory elements (PubMed:31691806). Required for brain development, probably by regulating expression of neuron-specific genes (By similarity). {ECO:0000250|UniProtKB:P0CH95, ECO:0000269|PubMed:19843542, ECO:0000269|PubMed:20023638, ECO:0000269|PubMed:20101266, ECO:0000269|PubMed:20208542, ECO:0000269|PubMed:20346720, ECO:0000269|PubMed:20421419, ECO:0000269|PubMed:20531378, ECO:0000269|PubMed:20548336, ECO:0000269|PubMed:20622853, ECO:0000269|PubMed:20622854, ECO:0000269|PubMed:31691806}. This is the function of ENSG00000172943 (PHF8, PHD finger protein 8).