Begin by graphing f(x)=2^{2} Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x)=2^{-x}

Question
Transformations of functions
asked 2021-01-15
Begin by graphing
\(\displaystyle{f{{\left({x}\right)}}}={2}^{{{2}}}\)
Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs.
\(\displaystyle{g{{\left({x}\right)}}}={2}^{{-{x}}}\)

Answers (1)

2021-01-16
Step 1
image
Step 2
Graph of \(\displaystyle{2}^{{{x}}}\) is shown as a dotted curve.
The graph of \(\displaystyle{2}^{{-{x}}}\) is the graph of \(\displaystyle{2}^{{{x}}}\) reflected in the y-axis.
Its asymptote has equation \(\displaystyle{y}={0}\)
0

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