Lysosomes have the function of digesting foreign materials and large structures, such as organelles. They do this by maintaining an acidic pH of approximately 5 and utilizing special proteins called acid hydrolyases, which are specifically designed to function at low pH levels. In order to maintain this low pH, lysosomes must be membrane-bound and have a highly regulated flow of protons.

Prokaryotes do not have membrane-bound organelles, including lysosomes.

Peroxisomes are primarily responsible for the breakdown of very long chain fatty acids and D-amino acids, as well as the synthesis of special types of phospholipids known as plasmalogens. If the cell cannot catabolize very long chain fatty acids, the issue is most likely within the peroxisomes.

The Golgi apparatus is very important for protein packaging. Mitochondria are crucial to generating energy for the cell. The smooth endoplasmic reticulum has various functions, including lipid and carbohydrate metabolism.

The function of breaking down cellular contents is done by the lysosome. Lysosomes have an acidic interior, which is useful for breaking down macromolecules that are no longer being used in the cell.

The smooth endoplasmic reticulum, in contrast, helps to break down foreign material, such as toxins. Mitochondria primarily serve to produce ATP for cellular energy. The Golgi apparatus works in tandem with the rough endoplasmic reticulum and helps to group and package proteins for vesicular transport.

Proton pumps use ATP to continuously pump hydrogen ions into the interior of the lysosome, thus maintaining an acidic environment in which the enzymes are most optimally efficient at breaking down the debris/macromolecules. The membrane of the lysosome is selectively permeable due to these types of transporters, and protects the rest of the cell from the very acidic environment. Recent journal articles suggest that the lysosome's membrane will be deliberately disrupted, releasing the acid and the hydrolases into the cytosol during apoptosis.

On its own, G-actin (globular actin) is not likely to nucleate and begin to form chains of F-actin (fibrous actin); therefore, it is useful to have proteins to help the nucleation process. One of these protein complexes is Arp2/3. Arp2/3 is especially known for its function of nucleating actin chains that branch off of previously established actin chains. Myosins are motor proteins that interact with actin chains to perform various functions, such as muscle contraction and transporting vesicles. Cofilin is a protein that binds G-actin monomers and helps them dissociate from F-actin.

Each choice describes a distinct function of the cytoskeleton. The cytoskeleton is involved in supporting various organelles, helping to anchor them in various locations around the cell and maintaining their shape and integrity. It also has the important function of helping with vesicle trafficking by associating with various motor proteins that carry vesicles from one part of the cell to another. The cytoskeleton is also a part of several different types of cell junctions (e.g. adherens junctions). Finally, the cytoskeleton is also an important part of various motile structures, such as cilia and flagella. 

The three major components of the cytoskeleton in cells are microtubules, intermediate filaments, and microfilaments. Microtubules are the larger filaments and make up the mitotic spindle, as well as flagella and cilia. Intermediate filaments are used in structural maintenance.

Microfilaments are the smaller filaments and make up the polymerized actin filament in muscle fibers.

Microfilaments and microtubules are both polarized, and can be used in vesicular transport. Intermediate filaments lack polarity and serve only structural functions.

Intermediate filaments form a veil right next to the nuclear membrane, are of intermediate thickness with respect to the other two cytoskeletal filaments, and they almost exclusively play structural roles. Actin filaments brace cells against surfaces and allow contractions in striated muscle. Also, actin filaments provide structural support and have a role in determining cell shape. Microtubules form the mitotic spindle and comprise cilia and flagella. They are also the "freeways" on which motor proteins move and transport vesicles throughout the cell.

GDP-GTP cycling can regulate a number of these cytoskeletal components, although GTP-binding is especially crucial to microtubule polymerization. In addition, microtubule polymers are comprised of alpha and beta tubulin, while this is not the case for the other components listed. Microtubules are the only choice that fit all of the criteria posed in the question.