# Begin by graphing f(x)=2^{2} Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x)=2^{-x}

Question
Transformations of functions
Begin by graphing
$$\displaystyle{f{{\left({x}\right)}}}={2}^{{{2}}}$$
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$\displaystyle{g{{\left({x}\right)}}}={2}^{{-{x}}}$$

2021-01-16
Step 1

Step 2
Graph of $$\displaystyle{2}^{{{x}}}$$ is shown as a dotted curve.
The graph of $$\displaystyle{2}^{{-{x}}}$$ is the graph of $$\displaystyle{2}^{{{x}}}$$ reflected in the y-axis.
Its asymptote has equation $$\displaystyle{y}={0}$$

### Relevant Questions

Begin by graphing
$$\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}.$$
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$\displaystyle{g{{\left({x}\right)}}}={2}^{{{x}\ +\ {2}}}$$
Begin by graphing
$$\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}.$$
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$\displaystyle{g{{\left({x}\right)}}}={2}^{{{x}}}={2}^{{{x}}}\ +\ {2}$$
Begin by graphing
$$\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}.$$
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}\ \cdot\ {2}^{{{x}}}$$
Begin by graphing
$$\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}$$
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
$$\displaystyle{g{{\left({x}\right)}}}=-{2}^{{{x}}}$$
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 vertical asymptote? Use the graphs to determine each functions domain and range. $$\displaystyle{g{{\left({x}\right)}}}=\ -{2}{{\log}_{{{2}}}{x}}$$
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. $$\displaystyle{g{{\left({x}\right)}}}=\ {{\log}_{{{2}}}{\left({x}\ -\ {2}\right)}}$$
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. $$\displaystyle{r}{\left({x}\right)}={{\log}_{{{2}}}{\left(-{x}\right)}}$$
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 vertical asymptote? Use the graphs to determine each function's domain and range. $$\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}\ {{\log}_{{{2}}}{x}}$$
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 vertical asymptote? Use the graphs to determine each function's domain and range. $$\displaystyle{g{{\left({x}\right)}}}=\ -{2}\ {{\log}_{{{2}}}{x}}$$
$$\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}$$
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}{{\log}_{{{2}}}{x}}$$