Question

Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x)=3^{x}=3^{x} - 1

Transformations of functions
ANSWERED
asked 2021-02-10
Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. \(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}={3}^{{{x}}}\ -\ {1}\)

Answers (1)

2021-02-11

\(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={3}^{{{x}}}\ -\ {1}\) Graph of g(x) can be obtained by translating the graph of f(x) by 1 unit downwards along the y-axis. \(\displaystyle\text{Domain of}\ {f{{\left({x}\right)}}}\ {i}{s}\ {x}\ \in\ {\left(-\infty,\ \infty\right)}\)
\(\displaystyle\text{Range of}{f{{\left({x}\right)}}}\ {i}{s}\ {\left({0},\ \infty\right)}\)
\(\displaystyle\text{Asymptote for the graph is}\ {y}={0}\)
\(\displaystyle\text{Domain of}\ {g{{\left({x}\right)}}}\ {i}{s}\ {x}\ \in\ {\left(-\infty,\ \infty\right)}\)
\(\displaystyle\text{Range of}{g{{\left({x}\right)}}}\ {i}{s}\ {\left(-{1},\ \infty\right)}\)
\(\displaystyle\text{Asymptote for the graph is}\ {y}=\ -{1}\) g(x) is the PURPLE curve, and f(x) is the RED curve image

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2020-11-23

Graph f and g in the same rectangular coordinate system. Use transformations of the graph f of to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. \(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ \text{and}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)

asked 2021-07-30
Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range.
\(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{-{x}}}\)
asked 2021-08-03
Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain arid range.
\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{x}}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}\)
asked 2021-08-09
Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes Use the graphs to determine each function's domain and range.
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)
...