Q.Explain the functions of the coupling and bypass capacitors?

These two capacitors do different jobs — one links stages, the other protects the gain. …

[!TLDR]

Coupling capacitor: transfers AC, blocks DC. Bypass capacitor: shorts AC around $R_E$ to preserve gain.

Both capacitors use the property that a capacitor passes AC but blocks DC. The coupling capacitor is placed in the signal path between stages (or at the input/output); it allows the amplified AC signal to move to the next stage while blocking the DC collector voltage, so the operating point of each stage is set independently. The bypass capacitor is connected across the emitter resistor $R_E$; it offers a very low reactance to AC, providing an easy path around $R_E$. This prevents AC negative feedback (which would reduce the voltage gain) while $R_E$ is still free to provide DC stabilisation. …