I have also question about this question? Q1.What factors mean that the potentiometer wiper position relating to k=o.5 is not necessarily equal to the mid point when measured outside the circuit? Q2. Set the input frequency to ,firstly 25kHz and secondly 200Hz and observe the variation in output amplitude at these frequencies as you vary the position of the potentiometer. Discusssion the action of the circuit at different frequencies in relation to the frequency-dependent gain profile seen in your plots.
If the pot is not linear (i.e. audio taper), k=0.5 will not be midpoint. However linear would be best.
However midpoint balances impedance ratio of gain so it is unity gain to nearly DC and well below audio range due to C2R4. Otherwise Pot to fixed ratio looks like 16 to 20 db boost or cut treble amp. Which is flat in the 25kHz range.
Since C is huge impedance compared to R1 and R2 in the low f range, gain is unity regardless of pot position.