ISM_T11_C01_F - Section 1.5 Combining Functions; Shifting...

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Section 1.5 Combining Functions; Shifting and Scaling Graphs 37 69. 70. 71. x y 72. x y * ± #& œ ##& Ê ± œ " "' ± ( œ ""# Ê ± œ " ## # # &$ % ( x x y y # # # # # # Š‹ È 73. x y 74. x y $ ± ²# œ$Ê ± œ" ±" ±# œ%Ê ± # # # # " # $ # ±± " ab x y x y # # # # # # # # È È ± 75. x y 76. x y ' '± ± *² œ & % abab ˆ‰ˆ‰ $" Ê ± Ê ± ÈÈ ± ’“ ˆ‰ È x y x y ±" #$ ' # $ ± # # # $ # # # " # #
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38 Chapter 1 Preliminaries 77. has its center at . Shiftinig 4 units left and 3 units up gives the center at h, k . So the x y # # "' * ± œ " !ß ! œ ²%ß $ ab a b equation is . Center, C, is , and major axis, AB, is the segment ± ab ab x 4 43 4 3 y 3 x y ±± ±² % ± $ # ## # # # ±œ " ʱœ " ² % ß $ from to . a b ²)ß $ !ß$ 78. The ellipse has center h, k . Shifting the ellipse 3 units right and 2 units down produces an ellipse x y # # %# & ± œ " œ !ß ! abab with center at h, k and an equation . Center, C, is 3 , and AB, the segment from a b œ $ ß²# ± œ" ± x 3 y ± & # # # to is the major axis. a b $ß $ $ß²( 79. (a) (fg)( x) f( x)g( x) f(x)( g(x)) (fg)(x), odd ²œ² ²œ ² œ ² (b) ( x) (x), odd Š‹ ff gg ( x ) g ( x ) g f( x) f(x) ² œœœ ² ± (c) ( x) (x), odd ˆ‰ ( x ) g ( x ) g ( x ) f ( x ) f ² ² ± (d) f ( x) f( x)f( x) f(x)f(x) f (x), even ²œ² ²œ œ (e) g ( x) (g( x)) ( g(x)) g (x), even # # ²œ ² œ² œ (f) (f g)( x) f(g( x)) f( g(x)) f(g(x)) (f g)(x), even ‰²œ ²œ² œ œ‰ (g) (g f)( x)
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This note was uploaded on 09/20/2010 for the course MATHEMATIC 09991051 taught by Professor Dr.maenshadeed during the Fall '10 term at Norwegian Univ. of Science & Technology.

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ISM_T11_C01_F - Section 1.5 Combining Functions; Shifting...

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