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)

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
asked 2021-02-21
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. \(\displaystyle{g{{\left({x}\right)}}}=\ {{\log}_{{{2}}}{\left({x}\ -\ {2}\right)}}\)

Answers (1)

2021-02-22

Step 1 Graph of \(\displaystyle{f{{\left({x}\right)}}}=\ {{\log}_{{{2}}}{x}}\) image 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. image

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