How to find transfer function looking bode plot
locate the 3db point. (The point where the line before and after the curve would meet.) Take note of the magnitude and frequency f.

Find the angular frequency at this point. w = 2 * pi * f

If the graph is going up then it's a zero. H(s) = w + s

If it's going down then it's a pole. H(s) = 1 / ( w + s )

Once you've got that. check the slope. If it's 20dB/decade then you're set. If it is 40, you'll need to square it, 60 and you'll cube it etc.

Finally you'll need to find the gain constant to make it correct at low frequency (or DC)

So you're answers will look like this:

H(s) = Gain * ( w + s )
H(s) = Gain / ( w + s )