If I have a piecewise function that I want to write an f(t) for then take the laplace transform;  f(t) = 0 t < 1 e^t-1 1 < t < 2 0 t > 2   How can I sketch this? And how do I find the Laplace transform ? And what does it mean when e is raised to t-1, is this a shift?

If I have a piecewise function that I want to write an f(t) for then take the laplace transform; 

f(t) = 0           t < 1

         e^t-1    1 < t < 2

         0           t > 2

How can I sketch this? And how do I find the Laplace transform ? And what does it mean when e is raised to t-1, is this a shift?