Answer
Domain :$\qquad(0,+\infty)$
Range :$\qquad(0,+\infty)$
Vertical asymptote: $\qquad x=0$
Work Step by Step
We start with the graph of $f_{1}(x)=\ln(x)$
(dashed blue).
Since y$=|\ln(x)|=|f_{1}(x)|$
its graph (red) is obtained by
reflecting the part of the graph of $f_{1}(x)$ where it is negative,
(the part below the x-axis, for $0