Question

Problems Set at an Oral Examination.
Construct the graphs of the following functions.
$y=lo{g}_2(2-x).$

Answer 1

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

For $y$ to be defined, $2-x>0⟹x<2$

At $x\to 2^{-},$ $y=-\infty$

At $x\to \infty$, $y\to \infty$

At $x=0$, $y={\log }_{2}2=1$

At $x=1$, $y={\log }_{2}1=0$