Question

Graph and give equations of all asymptotes Use the graphs to determine each function's domain and range f(x)=2^{x}\ and\ g(x)=2^{x-1}

Transformations of functions
ANSWERED
asked 2021-08-09
Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes Use the graphs to determine each function's domain and range.
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\ {\quad\text{and}\quad}\ {g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)

Answers (1)

2021-08-10
image
Both graphs are shown to the left.
The graph of g(x) is a translation to the right by 1 of the graph of f(x).
Both share a horizontal asymptote \(\displaystyle{y}={0}\)
The domain of both functions is R and range of both functions is \(\displaystyle{\left({0},\infty\right)}\).
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