$(1\mathrm{.}1)($a$)$ Write a MATLAB function signalx that evaluates the following signal at an arbitrary set of points:

$x(t)=\{\begin{array}{cc}2e^{t+2},& -3t-1\\ 2e^{-t}cos(2t),& -1t4\\ 0,& \text{e}\text{l}\text{s}\text{e}& \end{array}$

That is$,$ given an input vector of time points, the function should give an output vector with the values of $x$ evaluated at those time points. For time points falling outsicte $-3,4,$ the function should return the value zero.

$($b$)$ Use the function signalx to plot $x(t)$ versus $t,$ for $-6t6.$ To do this, create a vector of sampling times spaced closely enough to get a smooth plot. Generate a corresponding vector using signalx. Then plot one against the other.

$($c$)$ Use the function signalx to plot $x(t-3)$ versus $t.$

$($d$)$ Use the function signalx to plot $x(3-t)$ versus $t.$

$($e$)$ Use the function signalx to plot $x(2t)$ versus $t.$