Describing a Transformation In Exercises 53–58, g is related to a parent function f ( x ) = sin ( x ) or f ( x ) = cos ( x ) . (a) Describing the sequence of transformations from f to g . (b) Sketch the graph of g . (c) Use function notation to write g in terms of f . g ( x ) = 1 + cos ( x + π )
Describing a Transformation In Exercises 53–58, g is related to a parent function f ( x ) = sin ( x ) or f ( x ) = cos ( x ) . (a) Describing the sequence of transformations from f to g . (b) Sketch the graph of g . (c) Use function notation to write g in terms of f . g ( x ) = 1 + cos ( x + π )
Solution Summary: The author explains the sequential order of obtaining g(x) from the function.
Describing a Transformation In Exercises 53–58, g is related to a parent function
f
(
x
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=
sin
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x
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or
f
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x
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=
cos
(
x
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(a) Describing the sequence of transformations from f to g. (b) Sketch the graph of g. (c) Use function notation to write g in terms of f.
In Exercises 73–78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5
In Exercises 59–62, sketch the graph of the given function. What is the period of the function?
In Exercises 69–76, graph each function, not by plotting points, but by starting with the graph of one of the standard functions presented in Figures 1.14–1.17 and applying an appropriate transformation.
69. y = -sqrt(2x + 1) 70. y =sqrt(1-x/2)
71. y = (x - 1)3 + 2 72. y = (1 - x)3 + 2
73. y = 1 /2x - 1 74. y=(2/x2)+1 72. y = (1 - x)3 + 2
75. y = -(x )^(1/3) 76. y = (-2x)^(2/3)
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