Question

g is related to one of the parent functions. Describe the sequence of transformations from f to g. g(x) = 2 - (x + 5)^2

Transformations of functions
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asked 2021-05-25

g is related to one of the parent functions. Describe the sequence of transformations from f to g. \(g(x) = 2 - (x + 5)^2\)

Answers (1)

2021-05-26
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}\)
\(\displaystyle{g{{\left({x}\right)}}}={2}-{\left({x}+{5}\right)}^{{2}}\)
\(\displaystyle{f}{1}{\left({x}\right)}={f{{\left({x}+{5}\right)}}}={\left({x}+{5}\right)}^{{2}}\)
\(\displaystyle{f}{2}{\left({x}\right)}={f}{1}{\left({x}\right)}=-{\left({x}+{5}\right)}^{{2}}\)
\(\displaystyle{g{{\left({x}\right)}}}={f}{2}{\left({x}\right)}+{2}=-{\left({\left({x}+{5}\right)}^{{2}}\right)}+{2}\)
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