Question

Graph f and g in the same rectangular coordinate system.

Transformations of functions
ANSWERED
asked 2021-08-08
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.
\(\displaystyle{f{{\left({x}\right)}}}={3}^{{{x}}}\) and \(\displaystyle{g{{\left({x}\right)}}}=-{3}^{{{x}}}\)

Answers (1)

2021-08-09
image
The graph for \(\displaystyle-{3}^{{{x}}}\) is a reflection about the x-axis of \(\displaystyle{3}^{{{x}}}\).
The domain is all real numbers.
The range for \(\displaystyle{3}^{{{x}}}\) is all nonnegative numbers.
The range for \(\displaystyle{3}^{{-{x}}}\) is all nonpositive numbers.
The horizontal asymptote for both functions is \(\displaystyle{y}={0}\).
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