Final answer:
An ecclesial function of a district council is reviewing the qualifications of an assembly for affiliation with the district.
Step-by-step explanation:
An ecclesial function of a district council refers to a task or responsibility that the council has within a specific religious organization or denomination. Among the options given, the district council engaging in the review of qualifications for affiliation with the district would be considered an ecclesial function. This function would involve assessing whether an assembly or congregation meets the established requirements for becoming part of the district.
The other options mentioned can also be important functions of a district council, but they may not necessarily be considered ecclesial functions. For instance, reviewing qualifications of candidates for ministerial credentials and establishing qualifications for ministerial credentials are administrative functions related to credentialing within the religious organization. Investigating complaints made against a pastor might fall under the jurisdiction of a district council, but it is more of a disciplinary or judicial function.