Final answer:
The C-shaped tracheal cartilages prevent the trachea from collapsing, while the trachealis muscle and elastic membrane allow flexibility and help expel air or mucus during coughing.
Step-by-step explanation:
The function of the C-shaped tracheal cartilages is to provide structural support to the trachea. These cartilages maintain the open shape of the trachea, preventing it from collapsing and ensuring that air can pass through to and from the lungs.
The trachealis muscle and the elastic ligamentous membrane that complete each ring posteriorly support the trachea's flexibility. The trachealis muscle can contract, narrowing the trachea and aiding in the expulsion of air or mucus during coughing.
Additionally, the fibroelastic membrane's flexibility allows the trachea to stretch and expand slightly with each inhalation and exhalation, further aiding in efficient respiration.