Which core function of counseling is most closely associated with the terms "eligible and appropriate"?

The core function of counseling that aligns most closely with the terms "eligible and appropriate" is screening. Screening is a process utilized to determine if a client meets certain criteria that would make them suitable for a specific treatment or service, ensuring that they are both eligible and appropriate for the options available. This initial step is important as it helps in identifying the client's needs and determining the most suitable course of action or intervention that can provide them with the best chance for recovery.

While other functions like assessment and referral also focus on evaluating client needs and directing them to services, they operate at different stages in the care process. Assessment involves a more in-depth exploration of the client’s issues and background after initial eligibility is established, while referral pertains to directing clients to appropriate services. Consultation, on the other hand, typically involves discussion or collaboration with other professionals.

In summary, screening plays a critical role in establishing eligibility and appropriateness, making it the correct answer in this context.