How to determine the transform function of certain bode plots?
Bode plot 1: the low frequency gradient is +1, and we must assume that this gradient continues below 0.1 rad/sec (as we are not told anything to the contrary). Hence there is a free s term in the numerator.

There is a singularity at 8 rad/sec, hence a second order numerator term with zero damping. Two TF's have this characteristic - A and C.

Note: for a 3rd order term, if the product of the two inner coefficients equals the product of the outer two coefficients then it factorises to a 1st order root and a conjugate pair of imaginary roots.

In case A:
 \$ s^3+s^2+64s+64=(s+1)(s^2+64)\$, but A doesn't have a free s in the numerator, so the answer is C, where the numerator factorises to: \$s(s^2+64)\$

Use a similar approach for Bode plot 2. Note that the frequency scale for plot 2 is in Hz, and the critical frequencies need to be expressed in rad/sec to relate them to the TF coefficients.