Question

Functions f and g are graphed in the same rectangular coordinate system (see attached herewith). If g is obtained from f through a sequence of transformations, find an equation for g <img src="13310200082.JPG">

Performing transformations
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asked 2021-02-27
Functions f and g are graphed in the same rectangular coordinate system (see attached herewith). If g is obtained from f through a sequence of transformations, find an equation for g
image

Answers (1)

2021-02-28

image
We know function g(x) is obtained from f(x)
transformations we use for g(x) are
\(f(x)g=|x|\) reflection of f(x) with x-axis
\(\Rightarrow -∣x∣\)
then we shift our resultant graph by 5 units towards left on x axis
\(\Rightarrow -∣x−5∣\)
then at last shift the resultant graph by 1 unit towards upward
\(g(x)=-x∣x−5∣∣+1\)

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