Without a calculator, draw the graph of the following function including horizontal and vertical asymptotes, local maxima and minima, and inflection points.

$f(x)=\frac{(x-4{)}^2}{(x-2{)}^2},f^{\text{'}}(x)=\frac{4(x-4)}{(x-2{)}^3},f^{\text{'}\text{'}}(x)=\frac{8(5-x)}{(x-2{)}^4}$

with fully explanation please.