The network analyzer function of the Analog Discovery 2 USB oscilloscope makes it easy to characterize the function generator’s bandwidth—just connect the function generator to the input channel (making sure that the input channel is not specified as a reference) and do a sweep. The only choice is whether to use the wires that come with the basic unit or the optional BNC adapter board and scope probes. I tried it both ways (and with both 1X and 10X settings of the scope probes), using 1V amplitude on the waveform generator one in all cases:
I tried loading the function generator with resistors, but this made essentially no difference in the frequency characteristics. It isn’t the 1MΩ resistance of the scope that matters, but the capacitance of the oscilloscope plus probe.
So I tried adding capacitive loads and found that I got a very clear LC resonance. With a 330pF load, I got the peak near 10MHz to approximately cancel the drop:
A resonance around 9.1MHz with a 330pF capacitor implies an inductance of about 0.93µH, which is in a reasonable ballpark of the sort of inductance one would expect for 80cm of wire (4 wires each about 20cm).