6: Powering an op amp: Single or split supply, and "rail to rail"?
The most important criterion is that
the inputs to your circuit must not exceed the bounds of the power supplies.
For example in Fig 5a if you are using +15V - 15V for the supply then you can reasonably apply a 10 volt peak to peak sinewave and you will see the same at the output.
If the SAME op amp is used with a single supply (Fig 5b) +30V - 0V it wont work - and you will likely damage the IC - because the negative excursion of the AC input is outside the range of the supplies.
Bipolar op amps generally need a bit of "headroom" so for example in Fig 5a with ±15V supplies the input should be restricted to say 12V peak - peak.
A split supply doesnt need to be symmetrical as long as the inputs and expected outputs stay within the bounds of the supplies.
Generally CMOS op amps can happily accept "rail to rail" inputs (but check the data sheet). However when you read it offers rail-rail outputs you should be careful. The circuit will give outputs a few mV above the negative supply or below the positive supply - but only with a very high impedance load.