How can I determine by looking at the following tranfer function, that is this the transfer function of a band-pass filter:
You could guess the form of the frequency response of the filter if you knew the poles and the zeroes of any TF. Then drawing the poles and the zeroes in the complex plane you could tell something about that.
In your case there is no zero (numerator is constant). So you have a denominator which is a 3rd order polynomial. To find the poles you must find the roots of that polynomial, which are a function of the coefficients a,b,c.
Anyway, a 3rd order equation with real coefficients (assuming a,b,c are real) will have at least a real root and either another two real roots or a couple of complex conjugate roots.