Problem $2.$ Illustrating the point of discontinuity of a piecewise function is useful in models of the human visual system. The simple function $f(t)$ can be used to display one model of this discontinuity.

$f(t)=\{\begin{array}{cc}{t}^2,& -1t\frac{1}{\sqrt[\phantom{2}]{2}}\\ \frac{3}{2}-(t-\sqrt[\phantom{2}]{2}{)}^2,& \frac{1}{\sqrt[\phantom{2}]{2}}t3\end{array}$

where time, $t$ has $50$ equally spaced elements in each interval.

Create ONE main program that calls ONE user$-$defined function $($UDF$)$ with no inputs and one output matrix. It uses fprintf to write the matrix to an output file of choice.

The UDF

a$)$ Uses LaTeX to show $f(t)$; do NOT include the left brace.

b$)$ Creates one plot which shows the entire range.

Apply line types, line width and different colors of choice for each interval.

c$)$ Creates a column vector whose elements are any three values of time in the first interval.

d$)$ Creates a column vector whose elements are the corresponding three $f(t)$ values of the vector created in step $c.$

e$)$ Creates a matrix whose columns are the vectors in step $c$ and $d.$

Submit ALL files in ONE zipped folder that is labeled with your credentials.