$(10$ Points$)$ Use the SymPy P iecewise function to create a symbolic function x$($t$)$ with the

following expression:

x$($t$)=$

$$

$$

$$

t $+1,$ t in $[1,0)$

$1,$ t in $[0,1)$

$0,$ otherwise.

Use the SymPy plot function to plot x$($t$)$ in the range of t in $[2,2].$

ii $(10$ Points$)$ Use the SymPy method subs to create the following functions from x$($t$)$:

y$1($t$)=$ x$($t$)$

y$2($t$)=$ x$($t $1)$

y$3($t$)=$ x$($t $+1)$

y$4($t$)=$ x$(2$t$)$

y$5($t$)=$ x$($t$/2).$

Plot all ve functions above in the range of t in $[2,2].$ Describe, in layman$$s language, the

relationship between the plots of the above functions with the plot of x$($t$).$