Answer
Domain :$\qquad($0$,+\infty)$
Range :$\qquad(-\infty,+\infty)$
Vertical asymptote: $\qquad x=$0
Work Step by Step
We start with the graph of $f_{1}(x)=\log_{10}(x)$=$\log$x (dashed blue).
Since y$=1-\log_{3}(x)=-f(x)+1$
its graph (red) is obtained by
1. reflecting $f_{1}(x)$ about the x-axis, (green dotted),
2. then shifting up by 1 units.
Domain :$\qquad($0$,+\infty)$
Range :$\qquad(-\infty,+\infty)$
Vertical asymptote: $\qquad x=$0
