Writing down the step function

[Odyssey]

Hi there,

I'm stuck on getting my step function set up. the function is:

f(t)= 0, t<0
(a/b)*t, 0<t<b
a, t>b

where a and b are just constants.

Here's my step function of the first two intervals...the first one I didn't do anything to it since it's zero, so I got:

f(t)=u0(t)(a/b)*t

now I'm stuck on how to get the step function for the last interval.
I appreciate the help, thank you.

 

[interested_learner]

shift it

Think of it this way. You have a function x(t). This function would be x(0) at zero, right? But we want it to be x(0) at b not at zero, right? So what would we have to subtract off the t in x(t) inorder to get the function shifted over? ie x(t-?). Try out some values. Don't think too much, it is easy.

 

[Odyssey]

I'm guessing here, is it (t-b)?