Sketch the following functions and find the Laplace transforms:
A) LaTeX: f(t)=u(t)+3u(t-1)-2u(t-2)-2u(t-3).
B) LaTeX: f(t)=2u(t+2)-3u(t+1)+4u(t-1)-3u(t-2).
C) LaTeX: f(t)=tu(t)-(t-2)u(t-2)-2u(t-4).
D) LaTeX: f(t)=tu(t)-(2t-4)u(t-2)+(t-4)u(t-4).