To test a fax machine simply fax to somebody else with a fax machine – and have them send a reply fax back to you.
When sending the fax, turn on the confirmation page feature – a successful confirmation page shows that the fax machine on the other end has successfully received the message. Keep in mind that successfully sending does not necessarily mean that the fax machine will successfully receive a fax.
Here are some test numbers:
HP fax test number: +1-888-hpfaxme (1-888-473-2963) (source: http://support.hp.com/us-en/document/c00259105)
Canon fax test number: +1-855-FX-CANON (1-855-392-2666) (source: http://downloads.canon.com/support/testing-your-fax-machine.pdf)
Telstra fax test number: 1300 368 999 and 03 9640 0999 (source: http://goughlui.com/2013/02/13/telstra-fax-on-line-diagnostics-folds-test/)