g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. g(x) = -1/4 (x + 2)^2 - 2

nagasenaz 2021-09-10 Answered
g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. \(\displaystyle{g{{\left({x}\right)}}}=-\frac{{1}}{{4}}{\left({x}+{2}\right)}^{{2}}-{2}\)

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SabadisO
Answered 2021-09-11 Author has 27322 answers
We are starting with the parent function \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}\)
SETP 1: Vertically compress the graph by a factor of 2/3, to get \(\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}\)
STEP 2: Shift the graph by 4 units up, to get \(\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}+{4}\), which is the required function g(x)
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