Question on convolution
$$x(t)=\begin{cases}
 t+1\qquad &amp; 0\leq t\leq1 \\
 2-t\qquad &amp;  1&lt;t \leq2 \\
0\qquad &amp; \mathrm{elsewhere}
\end{cases}$$



$$f_1(t)=x(t+2)=\begin{cases}
 t+2+1\qquad &amp; 0\leq t+2\leq1 \\
 2-(t+2)\qquad &amp;  1&lt;t+2 \leq2 \\
0\qquad &amp; \mathrm{elsewhere}
\end{cases}$$

$$f_1(t)=x(t+2)=\begin{cases}
 t+3\qquad &amp;-2\leq t\leq-1 \\
 -t\qquad &amp;  -1&lt;t \leq0 \\
0\qquad &amp;\mathrm{elsewhere}
\end{cases}$$



$$f_2(t)=2x(t+1)=\begin{cases}
 2(t+1+1)\qquad &amp; 0\leq t+1\leq1 \\
 2(2-(t+1))\qquad &amp;  1&lt;t+1 \leq2 \\
0\qquad &amp;\mathrm{elsewhere}
\end{cases}$$

$$f_2(t)=2x(t+1)=\begin{cases}
 2t+4\qquad &amp; -1\leq t\leq0\\
 2-2t\qquad &amp;  0&lt;t \leq1 \\
0\qquad &amp;\mathrm{elsewhere}
\end{cases}$$



Now add them
$$y(t)=x(t+2)+2x(t+1)=\begin{cases}
 t+3\qquad &amp; -2\leq t&lt;-1 \\
3t+7\qquad &amp;t=-1\\
 t+4\qquad &amp;  -1&lt;t \leq0 \\
2-2t\qquad &amp;0&lt;t\leq1\\
0\qquad &amp;\mathrm{elsewhere}
\end{cases}$$

Now check $f_1(-1)=2$,$f_2(-1)=2$,also $y(-1)=f_1(-1)+f_2(-1)=4$