Question

g is related to one of the parent functions Describe the sequence of transformations from f to g. g(x) = 1/2|x - 2| - 3

Transformations of functions
ANSWERED
asked 2021-06-21

g is related to one of the parent functions Describe the sequence of transformations from f to g.

\(g(x) = \frac{1}{2}|x - 2| - 3\)

Answers (1)

2021-06-22

We are starting with the parent function \(f(x)=|x|\)
STEP 1:

Vertically compress the graph by a factor of \(\frac{1}{2}\), to get \(y=\frac{1}{2}|x|\)
STEP 2:

Shift the graph by 2 units to the right, to get \(y=\frac{1}{2}|x-2|\)
STEP 3:

Shift the graph by 3 units downwards, to get \(y=\frac{1}{2}|x-2|-3\), which is the required function g(x)

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