What would happen to the output of a function generator if you connected a 10Ω load to the output terminals? (Assuming you had it set up simply with a 1kHz output from the function generator showing a 2V p-p waveform on the oscilloscope).

 

It depends on the function generator.

You may very well burn up the output. 10 Ohms would be a very heavy load. I would use some sort of buffer/driver between the two.

 

Most FG are typically 50 ohms resistance in series with the load. You likely get 0.33Vpp.