Final answer:
The latent function of playing sports related to the options provided is the indirect instillation of values such as competition and respect. Latent functions are unintended positive consequences, and in sports, these include developing important life skills and social connections.
Step-by-step explanation:
The latent function of playing sports is not the obvious, intended outcomes such as increasing fitness or instilling values like competition and respect. Instead, latent functions are the unintended positive consequences that occur as a byproduct of the activity. Given the options provided, the latent function of playing sports would be most aligned with d) playing sports instills values such as competition and respect. While this choice might seem like a manifest function, the latent aspect comes into play as these values are indirectly developed through the process of engaging in sports and are not the primary objective of the sports themselves. The anticipation or intent of sports is typically focused on physical activity and teamwork, but the experience also creates a social framework where values like competition and respect are fostered.
Moreover, other latent functions might include social connections, developing time management skills, and learning to balance academics with extracurricular activities, which can be crucial life skills for college athletes. These benefits are not the explicit goals of sports programs, but they are beneficial byproducts that can have a significant impact on the lives of student-athletes.