Question

Problems Set at an Oral Examination.
Construct the graphs of the following functions.
$y=|lo{g}_{2}x|/lo{g}_{2}x.$

Answer 1

$y=\frac{|{\log }_{2}x|}{{\log }_{2}x}$

$y$ is not defined for ${\log }_{2}x=0$ that is for $x=1$

We know that ${\log }_{2}x$ is defined for $x>0$

Now, for $0<x<1$

${\log }_{2}x<0⟹y=-1$

${\log }_{2}x>0⟹y=1$