Answer
(a) $f(x)=\log_{2}{x}$
$GraphIII$
(b) $f(x)=\log_{2}{-x}$
$GraphII$
(c) $f(x)=-\log_{2}{x}$
$GraphI$
(d) $f(x)=-\log_{2}{-x}$
$GraphIV$
Work Step by Step
We know (Also mentioned in this chapter) that a $logarthmic$ function ($\log_{2}{x}$ ) has a form of Graph$III$. By applying transformations to these expressions we can determine their graphs too.
For a better understanding, we can consider $f(x)=\log_{2}{x}$ as a parent function.
(b)$f(x)=\log_{2}{-x}$
Applying this transformation to the parent function means to reflect the graph about $y$-axis, so its graph is Graph$II$
(c)$f(x)=-\log_{2}{x}$
This means reflection about $x$-axis, so its graph is Graph$I$
(d)$f(x)=-\log_{2}{-x}$
In this case we have to do reflections about both $y$-axis and $x$-axis. So this function has form of Graph$IV$
