Here's some info on the bloated bandwidth required for standard fax including the dot density. You can of course send a fax via your modem if you dial the real telephone number of the recipient.
A4 paper: 216mm (horizontal) * 297mm (vertical) normal mode 8dots/mm * 3.85dots/mm fine mode * 7.7dots/mm extra fine mode *15.4dots/mm
Each dot is either white or black and thus 1 bit. One sheet of A4 paper using fine mode is (216*8) * (297*7.7) = about 4 million dots. With a compression ratio of 8:1 it takes about 50 seconds at 9600bps for transmission.