Question

Graph f and g in the same rectangular coordinate system. Use the graphs to determine each function's domain arid range f(x)=e^{x} and g(x)=2e^{\frac{x}{2}}

Transformations of functions
ANSWERED
asked 2021-08-03
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 arid range.
\(\displaystyle{f{{\left({x}\right)}}}={e}^{{{x}}}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}\)

Expert Answers (1)

2021-08-04
The graph of \(\displaystyle{g{{\left({x}\right)}}}={2}{e}^{{{\frac{{{x}}}{{{2}}}}}}\) is streched horizontally from \(\displaystyle{e}^{{{x}}}\).
The domain of both functions if all real numbers.
The range of both functions is (0, infinit y)
The horizontal asymptote is \(\displaystyle{y}={0}\)
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