Begin by graphing f(x)= 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. g(x)=frac{1}{2} log_{2}x

Question
Transformations of functions
asked 2020-11-12
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. \(\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{2}}}}\ {{\log}_{{{2}}}{x}}\)

Answers (1)

2020-11-13
Step 1 image Step 2 The dotted curve is the graph of \(\displaystyle{{\log}_{{{2}}}{x}}\). The graph of \(\displaystyle{\frac{{{1}}}{{{2}}}}{{\log}_{{{2}}}{\left({x}\right)}}\ \text{is the graph of}\ {{\log}_{{{2}}}{x}}\ \text{stretched vertically by a scale factor of}\ {\frac{{{1}}}{{{2}}}}.\) Its asympote is the line \(\displaystyle{x}={0}\). It can be seen from the graph that the domain of the function is the set of all x to the right of the asymptote, that is \(\displaystyle{x}\ {>}\ {0}\). The range of the function is the whole of \(\displaystyle{\mathbb{{{R}}}}\).
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