Question

Construct the graphs of the following functions.
$y=lo{g}_2(x^2-2x+1).$

Answer 1

$y={\log }_2(x^2-2x+1)$

$⟹y={\log }_2(x-1{)}^2$

For, $y$ to be defined, $(x-1{)}^2>0⟹x\ne 1$

And for all $x\in R$ , $y$ is defined

$y=2{\log }_2|(x-1)|$

At, $x\to 1⟹y\to -\infty$

For, $x\to \pm \infty ⟹y\to \infty$

For $x=0,2⟹y=0$