\(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={3}^{{{x}}}\ -\ {1}\)
Graph of g(x) can be obtained by translating the graph of f(x) by 1 unit downwards along the y-axis.
\(\displaystyle\text{Domain of}\ {f{{\left({x}\right)}}}\ {i}{s}\ {x}\ \in\ {\left(-\infty,\ \infty\right)}\)

\(\displaystyle\text{Range of}{f{{\left({x}\right)}}}\ {i}{s}\ {\left({0},\ \infty\right)}\)

\(\displaystyle\text{Asymptote for the graph is}\ {y}={0}\)

\(\displaystyle\text{Domain of}\ {g{{\left({x}\right)}}}\ {i}{s}\ {x}\ \in\ {\left(-\infty,\ \infty\right)}\)

\(\displaystyle\text{Range of}{g{{\left({x}\right)}}}\ {i}{s}\ {\left(-{1},\ \infty\right)}\)

\(\displaystyle{P}{S}{K}\text{Asymptote for the graph is}\ {y}=\ -{1}\) g(x) is the PURPLE curve, and f(x) is the RED curve

\(\displaystyle\text{Range of}{f{{\left({x}\right)}}}\ {i}{s}\ {\left({0},\ \infty\right)}\)

\(\displaystyle\text{Asymptote for the graph is}\ {y}={0}\)

\(\displaystyle\text{Domain of}\ {g{{\left({x}\right)}}}\ {i}{s}\ {x}\ \in\ {\left(-\infty,\ \infty\right)}\)

\(\displaystyle\text{Range of}{g{{\left({x}\right)}}}\ {i}{s}\ {\left(-{1},\ \infty\right)}\)

\(\displaystyle{P}{S}{K}\text{Asymptote for the graph is}\ {y}=\ -{1}\) g(x) is the PURPLE curve, and f(x) is the RED curve