Why is this function BIBO stable?
Triangle inequality is your friend: if $y = a_1x_1+  a_2x_2+ a_3x_3 $, then $$|y| \le |a_1||x_1|+  |a_2||x_2|+ |a_3||x_3|$$
Hence if $x_{.}$ is bounded, the sum is bounded as well.