If you can get temporary access to a scope (e.g., friend, acquaintance, school), try the tests that alm outlined so that you gain some familiarity with how things should look or behave prior to testing an unknown device.
Regarding DMMs with waveform generation, some are able to do that (e.g., Keysight U1252A/B, U1282A). However, the probe compensation signal should be sufficient for confirming basic scope operation (unless, of course, the compensation signal generator is broken).