Answer
domain: $(-\infty,\infty)$
range: $(-1,\infty)$
asymptote: $ y=-1$
Work Step by Step
$ g(x)=e^{x}-1=f(x)-1$, so its graph is obtained by
shifting the graph of $ f(x)$ downward by 1 unit (the asymptote moves to $ y=-1$ )
Perform the transformation on the points given on the graph of f, and join the new points with a smooth curve (red, solid line).
domain: $(-\infty,\infty)$
range: $(-1,\infty)$
asymptote: $ y=-1$