Graph f and g in the same rectangular coordinate system. Use transformations of the graph f of to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x)=2^{x} text{and} g(x)=2^{x-1}

Graph f and g in the same rectangular coordinate system. Use transformations of the graph f of to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x)=2^{x} text{and} g(x)=2^{x-1}

Question
Transformations of functions
asked 2020-11-23
Graph f and g in the same rectangular coordinate system. Use transformations of the graph f of to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. \(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\text{and}{g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\)

Answers (1)

2020-11-24

Step 1 \(\displaystyle{f{{\left({x}\right)}}}={2}^{{{x}}}\text{and}{g{{\left({x}\right)}}}={2}^{{{x}-{1}}}\) Graph of g(x) can be obtained by translating the graph of f(x) by 1 unit tp the right along the x-axis. Domain of f(x) is \(\displaystyle{x}\in{\left(-\infty,\infty\right)}\) Range of f(x) is \(\displaystyle{\left({0},\infty\right)}\) Asympote for the graph is \(\displaystyle{y}={0}\) Domain of \(\displaystyle{g{{\left({x}\right)}}}={x}\in{\left(-\infty,\infty\right)}\) Range of PSKg(x) = (0, \infty) Asympote for the graph is \(\displaystyle{y}={0}\) image

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