Begin by graphing f(x)= \log_{2}x and then use transformations of this graph to graph the given function: h(x)=-1+ \log_{2}x

tricotasu 2021-08-05 Answered

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 functions domain and range.
\(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}\)

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Expert Answer

Aniqa O'Neill
Answered 2021-08-06 Author has 22130 answers

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

Step 2
image Answer: Graph of \(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}\). The graph is translated down 1 unit from the graph f(x).
The vertical asymptote is \(\displaystyle{x}={0}\). The x-intercept is (2,0. The domain of h(x) is \(\displaystyle{\left\lbrace{x}{\mid}{x}{>}{0}\right\rbrace}\). The range is all real numbers.
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