The only current way to send and receive faxes with a smartphone or tablet is through an online online fax service.
These services operate as a virtual fax machine located accessed through the internet. While apps are available for online fax services, they are not always necessary.
At this moment, there is no software on the market that lets a user physically connect a fax machine or printer to their smartphone or tablet so that the phone can act as the modem. As well, there is no option for a smartphone to use the same existing phone number to double as a fax line.
While there are applications that let a user print to a printer through their phone, there are none we are aware of that let a person fax through the same printer.