g is related to one of the six parent functions. a) Identify the parent function f. b) Describe the sequence of transformations from f to g. c) Sketch the graph of g by hand. d) Use function notation to write g in terms of the parent function f. g(x)= -2|x - 1| - 4

g is related to one of the six parent functions. a) Identify the parent function f. b) Describe the sequence of transformations from f to g. c) Sketch the graph of g by hand. d) Use function notation to write g in terms of the parent function f. g(x)= -2|x - 1| - 4

Question
Transformations of functions
asked 2021-01-10
g is related to one of the six parent functions.
a) Identify the parent function f.
b) Describe the sequence of transformations from f to g.
c) Sketch the graph of g by hand.
d) Use function notation to write g in terms of the parent function f.
\(\displaystyle{g{{\left({x}\right)}}}=\ -{2}{\left|{x}\ -\ {1}\right|}\ -\ {4}\)

Answers (1)

2021-01-11
a) Parent function: \(\displaystyle{f{{\left({x}\right)}}}={\left|{x}\right|}\)
b) Reflection in the y-axis
Vertical stretch by a factor of 2
Horizontal shift 1 unit to the right
Vertical shift 4 units downward
c) The graph will be
image
d) In function notation, \(\displaystyle{g{{\left({x}\right)}}}=\ -{2}{f{{\left({x}\ -\ {1}\right)}}}\ -\ {4}\)
0

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