a) Graph of \(\displaystyle{y}=-{\log{{3}}}{x}\)

b) Domain: (0,inf)

c) Ramge: (-inf, inf)

d) Asymptote: x=0

b) Domain: (0,inf)

c) Ramge: (-inf, inf)

d) Asymptote: x=0

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.

\(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{-{x}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{-{x}}}\)

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.

\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{x}}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{x}}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}\)

asked 2021-02-11

For \(\displaystyle{y}=\ -{{\log}_{{{2}}}{x}}\).

a) Use transformations of the graphs of \(\displaystyle{y}={{\log}_{{{2}}}{x}}\) and \(\displaystyle{y}={{\log}_{{{3}}}{x}}\) o graph the given functions.

b) Write the domain and range in interval notation.

c) Write an equation of the asymptote.

a) Use transformations of the graphs of \(\displaystyle{y}={{\log}_{{{2}}}{x}}\) and \(\displaystyle{y}={{\log}_{{{3}}}{x}}\) o graph the given functions.

b) Write the domain and range in interval notation.

c) Write an equation of the asymptote.

asked 2021-08-08

Begin by graphing \(\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}\).

Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range.

\(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}\)

Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range.

\(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}\)

asked 2021-08-01

Begin by graphing

\(\displaystyle{f{{\left({x}\right)}}}={\log{{2}}}{x}\)

Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each functions domain and range.

\(\displaystyle{r}{\left({x}\right)}={{\log}_{{{2}}}{\left(-{x}\right)}}\)

\(\displaystyle{f{{\left({x}\right)}}}={\log{{2}}}{x}\)

Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each functions domain and range.

\(\displaystyle{r}{\left({x}\right)}={{\log}_{{{2}}}{\left(-{x}\right)}}\)

asked 2021-09-28

Graph f and g in the same rectangular coordinate system. Use transformations of the graph off to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.

\(\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}{\quad\text{and}\quad}{g}⟨{x}{)}=−{\ln{{\left({2}{x}\right)}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={\ln{{x}}}{\quad\text{and}\quad}{g}⟨{x}{)}=−{\ln{{\left({2}{x}\right)}}}\)

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.

\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)