First find the transforms of the following functions. Then determine what type of characteristics they possess.

(a) \(f_{1}(t)=100 e^{-100 t} u(t)\)

(b) \(f_{2}(t)=1.25\left[e^{-100 t}-e^{-500 t}ight] u(t)\)

(c) \(f_{3}(t)=\frac{500}{9}\left[10 e^{-100 t}-e^{-10 t}ight] u(t)\)