The correct answer is master regulators promote the deposition of methyl or acetyl groups to mark inactive or active enhancers. Master regulators bind enhancer regions that have been created by pioneer factors to establish the chromatin state of the cell by deposition of methyl or acetyl groups on chromatin. Methylation correlates with inactive enhancers, whereas acetylation correlates with active enhancers. The fingerprint of active/inactive enhancers and its effect on gene expression establishes cell subtypes. Some, but not all master regulators function as pioneer factors to bind nucleosome rich DNA to promote euchromatin formation. 

Morphogens are proteins that can regulate the patterning of embryos over a multi-cell distance. Classic morphogens were discovered by injecting cytoplasm of embryos from the anteiror to the posterior, which would give rise to an animal with two heads. Injecting cytoplasm from the posterior to the anterior would give rise to animals with two posteriors. If injecting the RNA of a particular gene changes the patterning of the animal dramatically, it is likely a morphogen.

The only 'very anterior' structure listed among the answers is the head. If this particular hox gene is required to create the proper anterior appendage, we can predict that of the structures listed the head is most likely to be affected.

The correct answer is transcription factors. HOX transcription factors turn on genes during embryonic development to determine the type of segment structure (examples are legs or antennae) at different spatial regions of the embryo. Absence or mis-expression of HOX genes in early development renders misinformed or non-viable organisms. 

Multipotent cell types can give rise to a small number of cell types but have a restricted fate. This is in contrast to totipotent (zygote) or pluripotent cells (germ layers, iPS (induced pluripotent cells)) which can give rise to many different cell types, some that may make up very different parts of the body.

The correct answer is that asymmetric cell division begins the differentiation process from "parent" stem cells. Symmetric cell division generates two identical daughter cells that have mitotic spindles oriented parallel to the plane on which the cells reside. However, cells that begin a differentiation lineage undergo asymmetric cell division. The perpendicularity of the mitotic spindle in cells that eventually differentiate contributes to this process. 

Totipotent stem cells are the stem cells with the greatest potential of all stem cell types. A totipotent stem cell can give rise to any embryonic cell type, and can ultimately form an entire organism. Pluripotent stem cells can become any of the three embryonic germ layers, however, they do not have the capacity to form an entire organism because they cannot give rise to the extraembryonic tissue required for development, such as the placenta. 

The phosphorylation of Erk is the final step of the protein cascade of EGF pathway, and phosphorylated Erk enters the nucleus to increase transcription of genes that induce proliferation. If Erk is constitutively active, it will likely lead to higher proliferation rate.

Preventing EGF from binding to EGFR or disrupting EGFR's ability to enter the membrane would abolish EGF pathway activity and reduce proliferation. Likewise, abolishing kinase activity of RAF would terminate the signal transduction and lead to reduced proliferation.

Erythropoietin, released by the kidney, stimulates the production of red blood cells, which becomes necessary if circulating  has decreased. Tumor necrosis factor stimulates systemic inflammation and regulates the immune system. Transforming growth factor beta 1 controls cell growth, proliferation, differentiation and other processes. Interferon type II modulates immune functions. Interleukin 2 also modulates the immune cells.

Erythropoietin is a glycoprotein that is crucial for the production of red blood cells, a process also called "erythropoiesis." Each of the other answers contains a growth factor, but none of these have a primary function in red blood cell production.