$(10$ points$)($EXTRA CREDIT $1)$ Consider a continuous$-$time $($CT$)$ linear time$-$invariant $($LTI$)$ system with impulse response $h(t)$ shown in Figure $1.$

Figure $1$: Impulse response $h(t).$

Plot the output of this LTI system for the input $x(t)$ depicted in Figure $2.$

Figure $2$: Input signal $x(t).$

Note that to get full credit, make sure the breakpoints are clear. $($You do not need to write the function, you only need to plot.$)$

Hint$1$: Convolution is commutative and distributive: $x(t)**[h_1(t)+h_2(t)]=x(t)**h_1(t)+x(t)**h_2(t).$ It also can be generalized to more than two $h_{i}s.$

Hint$2$: You can also use the fact that convolving two pulses with different durations is a trapezoid as depicted in Figure $3.[$NO need to derive this convolution.$]$

Figure $3$: Convolution of two pulses.