What Transact-SQL function is used to perform a HyperLogLog function?

The use of the APPROX_COUNT_DISTINCT function is correct because it implements the HyperLogLog algorithm to provide an efficient way to estimate the number of distinct values in a dataset. This function is particularly beneficial for handling large datasets where exact count operations could be resource-intensive and time-consuming. APPROX_COUNT_DISTINCT leverages the HyperLogLog method to provide a probabilistic estimate of distinct values while utilizing significantly less memory compared to traditional counting methods, making it suitable for scenarios requiring quick analysis of large-scale data.

The other options do not represent the proper use of the HyperLogLog algorithm. COUNT_DISTINCT_APPROX, for instance, does not exist as a standard function in SQL Server. COUNT is a traditional function for counting rows but does not perform any approximate calculations. HYPERLOGLOG_COUNT is also not part of standard SQL Server functions. Therefore, the use of APPROX_COUNT_DISTINCT aligns accurately with the need for an effective HyperLogLog function in Transact-SQL.