Modem cannot be used by Mac OS X 10.10 (Yosemite) as dial-up or fax device

Problem:
Mac OS X 10.10 (Yosemite) discontinue support for many serial (USB) devices as dial-up or fax devices. Dial-up modems were previous allowed in the System Preferences->Network pane. Fax modems were previously allowed in the System Preferences->Prints & Scanners pane. Mac OS X 10.10.0 through Mac OS X 10.10.2 would not allow many modems or devices connected via USB-to-serial chipsets to be used in these ways.

Resolution:
Update to Mac OS X 10.10.3 or newer.