Variation of voltage gain with frequency
Depends of the schematic, for just a transistor it lowers with frequency, but in tipical amplifier it is c). At lower frequencies if coupled with capacitor gain is low because of reactance of that capacitor. At high frequencies it is lower because of transistor gain. If it is DC coupled, than have low gain only on high frequencies.

http://elearning.vtu.ac.in/P9/notes/06ES32/Unit6-MSS.pdf

EDIT: after your update, definitely it is answer C. At lower frequencies you have losses in capacitor before Rb (at frequency 0, it have infinite reactance).

You can see input section: It consist from capacitor, resistor and base-emiter diode (you can think of it as a resistor in this case). Resistance (reactance) of capacitor is $$ Xc = \frac{1}{2\pi f C}$$ So resistance of capacitor changes (lowers) with frequency. At low frequencies it is very high, so input signal is divided between it, resistor and base junction and only small part of input signal is "seen" at base junction which is then amplified. Because of that you will have lower output signal at low frequencies.

At higher frequencies, input capacitor influence is negligible, so circuit amplification depends only on transistor which have lower gain at high frequencies.

In the middle reactance of the capacitor is small and also gain of transistor is high, so your gain would be high.

EDIT2:
You also have capacitor on output which will also lower gain of low frequencies (similar as input capacitor because of high resistance (reactance)).