A systems administrator is creating a backup copy of the /home/ directory.

Creating backups is a core responsibility in Linux system management, and the Linux+ V8 objectives emphasize proper use of archiving and compression tools. The tar utility is the standard Linux tool for creating archive files, and it also supports compression through various options.

The command tar -cJf /backups/home.tar.xz /home/ correctly combines both archiving and compression in a single step. The -c option creates a new archive, -J specifies XZ compression, and -f allows the administrator to define the output file name. This results in a compressed archive of the entire /home/ directory, which is efficient for storage and transfer.

The other options are incorrect. cpio is an archiving tool but does not perform compression by itself without additional commands or pipelines. rsync -z compresses data during transfer but does not create an archive file. The dd command performs low-level copying of raw data and is not suitable for directory-based backups.

Linux+ V8 documentation highlights tar as the preferred utility for filesystem backups due to its flexibility, reliability, and support for multiple compression algorithms. Therefore, the correct answer is C.