Final answer:
The statement about the organelle that houses the cell's genetic material and regulates cell functions being the nucleus is true. The nucleus, found in eukaryotic cells, is the control center that contains DNA organized into chromosomes which guide all cellular activities.
Step-by-step explanation:
The statement is true: the organelle that contains the cell's genetic material (i.e. DNA) and is vital to the regulation of all cell functions is the nucleus. The nucleus is a membrane-enclosed organelle found in eukaryotic cells, and it is the largest organelle in the cell. It holds most of the cell's genetic information, which is organized into chromosomes. These chromosomes encode the genetic instructions that are necessary for all cellular activities, including the synthesis of RNA and proteins. The regulatory role of the nucleus is due to its control over gene expression, which impacts protein synthesis and thereby directs the functions and activities of the cell.
Within the nucleus, the DNA is combined with proteins to form chromatin, which condenses into chromosomes during cell division. Additionally, the nucleus contains the nucleolus, which is involved in ribosome synthesis. The nuclear envelope, a double membrane with nuclear pores, surrounds the nucleus and controls the transport of materials into and out of the nucleus, maintaining the environment necessary for gene expression and DNA replication. Thus, the nucleus can be likened to the control center or command center of the cell, orchestrating cellular processes through the genetic material it contains.