Answer
$\text{Domain: }
(-\infty, \infty)
\\\text{Range: }
(-\infty,3)
\\\text{Horizontal Asymptote: }
y=3$
Work Step by Step
The black graph is the graph given in Figure 2, $y=
10^x
$.
The red graph is the graph of the given function, $
f(x)=3-10^{x-1}
$. It is the result of shifting the black graph by $1$ unit to the right, reflecting about the $x-$axis, and shifting $3$ units up.
The red graph has the following characteristics:
\begin{array}{l}\require{cancel}
\text{Domain: }
(-\infty, \infty)
\\\text{Range: }
(-\infty,3)
\\\text{Horizontal Asymptote: }
y=3
.\end{array}