If I have a two channel function generator, can I add the output voltage of both channels to double my output voltage? For example, if my function generator’s channel 1 goes up to 20 Vpp, and channel 2 goes up to 20 Vpp, can I add the two channels to get 40 Vpp? If so, do I do something with the sync? If not, what is the sync used for?
Nearly all function generators produce output referenced against the system's ground-- and thus the "black lead" on your function generator's output is connected to the system's ground. If you tried to put those two channels in series, you'd inadvertently be shorting one of the output channels to ground! (Contrast this to the many power supplies with "floating" outputs, whose current returns aren't tied together, or to ground.)
If you'd like to produce an increased voltage output, you'll likely want to amplify the signals after they leave your function generator. If you'd like to add the two channels together for reasons beyond simply increasing your peak-to-peak output voltage, you might want to look into summing amplifiers.
[Edit: It's also worth mentioning that most function generators can produce amplitudes that are "twice as large" when driving high-impedance loads, compared to 50-ohm loads. This is a result of the 50-ohm output impedance of these generators; for a 50-ohm load, the output and load impedances are matched, and thus half of the voltage is dropped over the output impedance. To provide an accurate display of voltage dropped over the load, most function generators halve their display when put in 50-ohm load "mode".]
If not, what is the sync used for?
The synchronization waveform is designed to produce a waveform which produces a transition each time the function generator begins a new cycle of output-- this allows you to easily "sync up" another piece of equipment, such as your oscilloscope-- which can be set to trigger on a rising or falling edge of the synchronization signal.
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