raacampbell:
Ummm... . What I didn't understand was why I need negative voltages with respect to ground in this particular case.
You don't - as long as the op-amp is designed for "rail to rail" drive. If it isn't, then if it cannot drive to ground, you need to connect its negative supply terminal to a suitable negative voltage supply to compensate for this, and correspondingly if it is unable to drive to the positive rail, you need a positive supply of more than 5V.
The non-inverting input needs to be tied to exactly half the voltage range you wish to invert, and the resistors to the inverting input need to be equal. In fact, all four resistors need to be equal so that both inputs "see" the same impedance.
Oh - are you sure the function generator is not AC coupled?