$y(t) = 1 - e^{-t}$ for $t<1$ and $y(t) = e^{1-t} - e^{-t}$ for $t \geq 1$

$y(t) = t e^{-t}$ for all $t$

$y(t) = 1 - e^{-t}$ for $t<1$ and $y(t) = (e-1)e^{-t}$ for $t \geq 1$

$y(t) = e^{-t}$ for $t<1$ and $y(t) = 1 - e^{-t+1}$ for $t \geq 1$