I'm using a function generator that has a 50ohm internal resistance. Does this affect any circuit that I may connect it to and if so, how would it affect the results?
The 50 Ohm internal resistance changes the behavior from that of an ideal signal source is one simple manner: It behaves just like adding a 50 Ohm resistance in series with the voltage source, completing the circuit through your load:
As the function generator is specified with an internal resistance of 50 Ohms, its signal specifications would be for a 50 Ohm load.
For example, for a 5 Volt signal output setting, and using a matched 50 Ohm load for X above, the current through the loop will be:
I = V / R = 5 / 100 = 50 mA. This is the nominal, specified case. As load 'X' is changed, the current drawn will change, and thus the voltage across the load changes correspondingly.