Question

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?

Transformations of functions
ANSWERED
asked 2021-08-08
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.
\(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{x}}\)

Answers (1)

2021-08-09
\(\displaystyle{h}{\left({x}\right)}=-{1}+{{\log}_{{{2}}}{\left({x}\right)}}\) can be obtained from the graph of \(\displaystyle{{\log}_{{{2}}}{\left({x}\right)}}\) by translating it along the x-axis by 1 unit in the downward direction
In the graph below:
The blue dotted curve represents the graph for \(\displaystyle{y}={{\log}_{{{2}}}{x}}\)
The black solid curve represents the graph for \(\displaystyle{y}=-{1}+{{\log}_{{{2}}}{x}}\)
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