# Laplace Transform - Step Functions

1. Jun 24, 2008

1. The problem statement, all variables and given/known data
Please help by explaining in detail how to find the Laplace transform of the function

f(t) = { 2 0 <= t < 3
{ -2 t >= 3.

2. Relevant equations

3. The attempt at a solution
For the most part I know that U(t-3)(t-3).

I want to account for the amplitude of 2 like this but I think that I am wrong.

2-2U(t-3)*-2(t-3). I feel that I'm on the right track but might have set up the problem incorrectly. if I have it set up correctly I think I can go from there but would like directional help please.

Thank You,

2. Jun 24, 2008

### Defennder

No I don't think that is correct.

In general, if

$$f(t)= g(t) \ \mbox{for} \ a\leq t \leq b$$ and is zero everywhere else, then

$$f(t) = g(t)[u(t-a) - u(t-b)]$$.