laplace transform graphs

[Lorenz]

I'm having trouble graphing these. I'm not sure if I'm doing it right

My attempt. I think I did the last two right?

 

[tkhunny]

1) There probably shoudl be some curvature in your t^2.
2) Why does it quite at t=2?
3a) I think you mean 7 < t
3b) Why does it quite at t = 7?
4a) Where is 1 on [0,2)?
4b) Rather overshot t = 5, didn't you?
4c) Why does it quite at t = 5?