My teacher says that this signal is DC, but if the polarity varies from 0V to -8V , shouldn't it be AC?
He says that
DC + AC = DC
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DC + AC = DC
Plainly put: No.
It's AC with a DC offset, if you will.
This is less about whether the sign changes (that sign is just relative to some arbitrarily defined reference), but about whether the energy transport happens mainly in the DC or AC component.
That's all that makes the difference between "AC with DC offset" and "DC with AC ripple".
It has both AC and DC components. Which of these you regard as "the signal" depends on its intent (i.e. on the information content).
If it is say analogue audio with some DC in there for some reason, then it is an AC signal with a DC offset or bias.
But if it is say a relay control line picking up interference from somewhere, then it is a DC signal with AC noise present.
You can see this difference of viewpoint among other answers offered here.
But be wary of hitting your teacher over the head in such cases; check the answer expected for the exam, as teachers are more focused on getting you through that than they are on the ultimate truth.
This is really a terminology question. For instance, Wikipedia has a classification under which your signal would be called either "Alternating" or "Pulsating":
Clarify with your teacher what is his definition of AC and DC, and then apply those definitions to the signals you need to classify.
Understand that such classification for arbitrary signals is descriptive rather than strict. There is no special Ohm's law for pulsating current. There are formulas/models which only work in special cases, such as constant voltage / current (which you would colloquially call DC) or for a periodic sinusoidal signal with zero offset (which you'd call AC). Obviously, the models which assume constant voltage won't apply to your signal, even if your teacher calls it DC.
EVERY signal contains components of both AC and DC. The issue is one of dominance. Which of these components dominates the signal content.
A "DC" power source is likely to contain a small amount of noise or "ripple". The noise/ripple will be AC however the dominant component will be the DC offset.
An "Audio signal" might contain a small DC offset. The signal will be primarily AC, but will contain a small amount of DC.
It is varying with time and also goes below zero, for all the definition is AC.
For some (few) people if a signal is always positive or always negative it could be defined DC (since the direction stays the same).
For all the practical uses DC is fixed, constant and only with some ripple or noise (if acceptable)
Your question is a contradiction:
If the polarity varies from 0V to -8V , shouldn't it be AC?
If the VOLTAGE ranges between 0V and -8V then the polarity doesn't vary.
Furthermore your drawing says 10V not 0V, so your green graphline should be under the blue line.
VDC + VAC = VDC if only |VDC| >= VAC