Answer
please see image:
Work Step by Step
We start with the graph of $f_{1}(x)=\log_{10}(x)$ (dashed blue).
Since $f(x)=-\log_{10}(x)=-f(x)$
its graph (red) is obtained by reflecting f(x) about the x-axis.
Domain of $f$:$\qquad(0,+\infty)$
Range of $f$:$\qquad(-\infty,+\infty)$
Vertical asymptote: $\qquad x=0$
