Here is my answer:
step(t-1)-6*step(t-3)+9*step(t-5)
but it's wrong!!
help!!
Note as quick check when you evaluate at $\displaystyle t=4$ you get
$\displaystyle f(4)=1-6+0=-5$
Just "turning on" the next part is not enough you need to "turn off" the first part as well.
Let $\displaystyle S(t)$ be the unit step function then
$\displaystyle f(t)=S(t-1)-7S(t-3)+15S(t-5)$
Note to fit the turn on and off analogy from above
$\displaystyle f(t)=S(t-1) - S(t-3)-6S(t-3)+6S(t-5)+9S(t-5)$
When you simplify it is the same as above.