Answer
Please see below.
Work Step by Step
The graph of $h(x)=- \ln (x)$ (the red graph) is the graph of $f(x)=\ln x$ (the blue graph) reflected about the $x$-axis.
Looking at the graph, we observe that the vertical asymptote is $x=0$.
We also find that the domain and the range of the function $h(x)$ are$$D_h=(0, \infty ) \quad \text{ and } \quad R_h= (- \infty, \infty ),$$respectively.
