Answer
1st step (black graph): The parent function: $3^x$
2nd step (green graph): Shifted 1 unit to the right. $3^{x-1}$
The domain is $(-\infty,\infty)$
The range is $(0,\infty)$
The horizontal asymptote is y=0.
Work Step by Step
The domain is a horizontal span from the function's smallest value of x to the function's largest value of x. If there is a discontinuity, the domain must show where the discontinuity happens. In the case of exponential functions, there are no discontinuities, so the domain goes from negative infinity to positive infinity.
The range is a vertical span from the function's smallest value of f(x) to the function's largest value of f(x). In the case of exponential functions, there is always a horizontal asymptote which sets the lower or higher boundary of the range.
Horizontal asymptotes are horizontal lines that approach a graph but never intersect it.