calculus1-3b

Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Edition)

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Section 1.3 Combining Functions; Shifting and Scaling Graphs 19 62. Let y f x Let g x x , h x x , and i x x f x œ " œ Þ œ œ # œ # œ " œ Þ È È a b a b a b a b a b a b a b a b x x # # "Î# "Î# "Î# " # È The graph of g x is the graph of y x reflected across the x-axis. The graph of h x is the graph of g x shifted right a b a b a b È œ two units. And the graph of i x is the graph of h x compressed vertically by a factor of . a b a b È # 63. y f x x . Shift f x one unit right followed by a shift two units up to get g x x . œ œ œ " # a b a b a b a b $ 3 64. y x f x . Let g x x , h x x , i x x , and œ " B # œ Ò " # Ó œ œ œ " œ " # a b a b a b a b a b a b a b a b a b a b $ $ $ $ $ j x x . The graph of h x is the graph of g x shifted right one unit; the graph of i x is the graph of a b a b a b a b a b a b œ Ò " # Ó $ h x shifted down two units; and the graph of f x is the graph of i x reflected across the x-axis. a b a b a b
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20 Chapter 1 Functions 65. Compress the graph of f x horizontally by a factor of 2 to get g x . Then shift g x vertically down 1 unit to
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