Begin by graphing f(x)= 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. g(x)= log_{2}(x - 2)

Question
Transformations of functions
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. $$\displaystyle{g{{\left({x}\right)}}}=\ {{\log}_{{{2}}}{\left({x}\ -\ {2}\right)}}$$

2021-02-22

Step 1 Graph of $$\displaystyle{f{{\left({x}\right)}}}=\ {{\log}_{{{2}}}{x}}$$ Step 2 Graph of $$\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{\left({x}\ -\ {2}\right)}}$$ From $$\displaystyle{{\log}_{{{2}}}{x}}$$ the graph is translated to the right 2 units. The x-intercept is (3, 0). There is a vertical asymptote at $$\displaystyle{x}={2}$$. The domain of the graph is $$\displaystyle\le{f}{t}{\left\lbrace{x}{\mid}{x}\ {>}\ {2}{r}{i}{g}{h}{t}\right\rbrace}.$$. The range is all real numbers.

Relevant Questions

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 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 vertical asymptote? Use the graphs to determine each function's 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 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
$$\displaystyle{f{{\left({x}\right)}}}={2}^{{{2}}}$$
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.
$$\displaystyle{g{{\left({x}\right)}}}={2}^{{-{x}}}$$
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.
$$\displaystyle{g{{\left({x}\right)}}}=-{2}^{{{x}}}$$
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2},{g{{\left({x}\right)}}}={2}+{8}{x}-{4}{x}^{{2}}$$
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.
In the following items, you will analyze how several transformations affect the graph of the function $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$. Investigate the graphs of $$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}},{g{{\left({x}\right)}}}={f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}+{2}}}},{h}{\left({x}\right)}={\frac{{{1}}}{{{x}-{2}}}},{p}{\left({x}\right)}={\frac{{{1}}}{{{x}-{4}}}}\ \text{and}\ {z}{\left({x}\right)}={\frac{{{1}}}{{{x}^{{{2}}}+{1}}}}$$. If you use a graphing calculator, select a viewing window $$\displaystyle\pm{23.5}$$ for x and $$\displaystyle\pm{15.5}$$ for y. At what values in the domain did vertical asymptotes occur for each of the functions? Explain why the vertical asymptotes occur at these values.