Find the greatest and least value of the function $f\left(x\right)=\left|\frac{1+x}{1-x}\right|$ in $[-2,0]$ and also sketch the graph of
$f\left(x\right)$ and find its range.

$f\left(x\right)=[\begin{array}{rl}\frac{1+x}{1-x}& \text{if}-1\le x<1\\ \frac{x+1}{x-1}& \text{if}x>1 \text{or }x<-1\end{array}$

$f^{\mathrm{\prime }}\left(x\right)=[\begin{array}{ccl}\frac{2}{(1-x{)}^2}& \uparrow & \text{in}(-1,1)\\ \frac{-2}{(x-1{)}^2}& \downarrow \text{i n }x>1 \text{or }x<-1& \end{array}$

Range in $[0,\propto ).$

Maximum value in [–2, 0] occurs at x = 0 and f(0) = 1; 

Minmum value in [–2,0] occurs at x = – 1 and f(–1) = 0