The figure below depicts the generating function $g(x)$ used in a Simple Fixed$-$Point iteration algorithm $($and a $45$ line for reference$).$

$($a$)(6$ points$)$ Starting at a value of $x0=3,$ give $x1,x2,x3,$ and $x4$ generated by the fixed$-$point method. Show your work directly on the plot below.

$($b$)(8$ points$)$ Give the values of the approximate percent relative error, $E_a$ in the first $4$ steps of the fixed$-$point algorithm, based on your values from part $($a$)$

$($c$)(6$ points$)$ Is the method converging or diverging? Do the graphical results agree with the theory covered in the course $($Fixed Point Theorem$).$ Please discuss in the space below.