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Section 4.9 In a relation described by a sentence in x and y, the following processes yield the same graph: xh yk 1. replacing x by and y by in the a b sentence; 2. Applying the scale change (x,y) (ax,by) where a, b≠ 0, followed by the applying the translation (x,y) (x + h, y + k) to the graph of the original relation. yk xh sin( ) has b a Notice : to use this formula, Amp: |b| Period: 2π *|a| x must be by itself! Phase shift: h Vertical shift: k Describe the graph of y = sin (2x – π/4) y = sin (2(x – π/8)) Amp: 1 Period: 2π/2 = π Phase shift: π/8 to the right Vertical shift: 0 The composite of what scale change and translation maps y = cos x onto y = 3 cos 4(x + π) – 10 S(x,y) (x/4, 3y) T(x,y) (x – π, y – 10) x4 y 2 sin( ) 4 S(x,y) (4x, 2y) T(x,y) (x + 4, y) Amp 2 Period 2π * 4 = 8π Vertical shift 0 Phase shift 4 to the right y = 2 sin (3x + π) + 2 y = 2 sin 3(x + π/3) + 2 S(x,y) (x/3, 2y) T(x,y) (x - π, y + 2) Amp 2 Period 2π * 1/3 = 2π/3 Vertical shift 2 up Phase shift π/3 to the left Pages 290 1 , 3 – 6, 9 – 11 *Don’t need to graph