MATLAB Code, please do $*$exactly$*$ as instructions and code says

b$)$ Where indicated below, complete the function, linspline$(),$ which takes two input vectors of data points $x$ and $y,$ of any length $n($either both column or row$),$ and scalar input,

a$.$ It computes output, s$,$ which is $S_{k-1}(a),$ the linear function, $S_{k-1}(x),$ evaluated at a:

$S_{k-1}(a)=y_{k-1}+\frac{y_k-y_{k-1}}{x_k-x_{k-1}}(a-x_{k-1})$ where $aison{x}_{k-1},x_k.$

$($This function is one linear function $($i$.$e$.,$ one line$)$ in the piecewise linear function on the entire interval, $x_1,x_n$ :

$S(x)=\{\begin{array}{ccc}{S}_1(x),& [x_1,& x_2)\\ S_2(x),& [x_2,& x_3)\\ S_3(x),& [x_3,& x_4)\\ \text{v}\text{d}\text{o}\text{t}\text{s}\text{,}\\ S_{n-1}(x),& [x_{n-1},& x_n]\end{array}$

i$)$ The function linspline$()$ will first search for the value of $k,$ where $x_{k-1}a{x}_k.$ To accomplish this, linspline$()$ will call a modified version of the binary search function

disussed in class. Modify the code per the instructions in the comments below.

ii$)$ Then, the code will evaluate $S_{k-1}(a)$ for just the interval $x_{k-1},x_k.$ For example, if the value of a were between $x_7$ and $x_8(k=8),$ then it would only evaluate $s=$

$y_7+\frac{y_8-y_7}{x_8-x_7}(a-x_7).$ Assume that $x_{1}a{x}_n$ and $x_1,x_2,$dots,$x_n{x}_1,$ but that $x_1,x_2,$dots,$x_n$ are not necessarily evenly$-$spaced.