Consider the following zero$-$state input$-$output relations for a variety of systems. In each case, determine

whether the system is zero$-$state linear, time invariant, BIBO stable and$/$or causal.

$($a$)$ y$($t$)=5$f$($t$)$u$($t$).($b$)$ y$($t$)=$$($t$4)$f$2($t$).$

$($c$)$ y$($t$)=$Rt$2$f$($$)$d$.$

$($d$)$ y$($t$)=$f$($t$1)+$f$($t$+1).($e$)$ y$($t$)=$ f$(2$t$).$

$($f$)$ y$($t$)=($t $+1)$f$($t$).$