Question

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

Transformations of functions
ANSWERED
asked 2021-05-18
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

Expert Answers (1)

2021-05-19
We are starting with the parent function \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}\)
STEP 1: Vertically compress the graph by a factor of \(\displaystyle\frac{{1}}{{4}}\), to get \(\displaystyle{y}={\left(\frac{{1}}{{4}}\right)}{x}^{{2}}\)
STEP 2: Reflect the graph across x-axis, to get \(\displaystyle{y}=-{\left(\frac{{1}}{{4}}\right)}{x}^{{2}}\)
STEP 3: Shift the graph by 2 units to the left, to get \(\displaystyle{y}=-{\left(\frac{{1}}{{4}}\right)}{\left({x}+{2}\right)}^{{2}}\)
STEP 4: Shift the graph by 2 units downwards, to get \(\displaystyle{y}=-{\left(\frac{{1}}{{4}}\right)}{\left({\left({x}+{2}\right)}^{{2}}\right)}-{2}\) which is the required function g(x)
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