1.6(one) - 1.6 Transformation of Functions.Hx I)” Library...

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Unformatted text preview: 1.6 Transformation of Functions .Hx): I)” Library Functions: Cfltfléiflill melimt identity Funetinn Margin“: *‘ahw Fla-mm: .r ) ' Umngziu: 3' W n a"; ' Dnmamfi my: 9’ Qumran: a; avg-1: 1' .1 util w? 229': 3hr!" , , . . u R a?” Eu“ “1;” mm '“ '7 1* Rama): [Etna m; *3 Emma: U. A): '9 If“ x'f‘ 1| :‘w; T’\-', . . , _. _ . _ V. “n da' m' K v " lecmufimfl mi Ewan-g 1:32;; *‘ IE-acguaamfi gm 3 - '34, 13} and 4..) ‘- ,. ‘_ 4 immasing {1:1 {1%. 42-21:: I Than fuming; K, .1 m . E * mam;er *1" hwsu Eunrmm flffififianfl Qttafimfic Parkman S‘BEW 3360‘ WWW galleriain Calais: Functimn (r ‘ y 1' 15mm: {hwy}. ix"); ' Drum-311: 2'14 “1.. r EF. 3,; 4* Uliilzil'i-Qlifii i "22 I3 ' Ragga: {Mg}; ' Range; ; * Range; {anew} 1* Dikffi’tfigfii‘éig m1 {-szgl’l-fx am; ‘ Elli‘l’fiafiingim{3.57:3} g, {Humming GEE {mam {Winning an WAG: l‘ Yuma I‘um‘iinn '1' Mimi}!!ng Hm i gigj'lcggfigg ti'irkm fr: mat lino-micro Reciprocai Function .i, " Hamid!“ 3;} Domain: (-O0,0)U(0,00) j. Rim‘w- R" “if”? Range: (-O0,0)U(0,00) Decreasing on (-00,0) and (0,00) '- E‘Eahi l'itmdriiun Odd function " 1*E'I£T¥’~i.’:.5.fi.‘ifi§‘lgt§Hf: NJ} 0 ((01)?) A a. ) lzx 01%» rm) ‘1 l.Vertical shifts H _ Xha/D (ha) a— 2 3 : X —- 3 - f(x) + c shifts the graph of f up by ‘c’ units (effect on the coordinates is to add c to each of the y-coordinates of the original points) 0 f(x) — c shifts the graph of f down by ‘6’ units (effect on the coordinates is to subtract c from each of the y-coordinates of the original points) 2. Vertical Stretches and Shrinking (Compressions) o If e > I, c*f(x) stretches the graph of f vertically by a factor of “c” (effect on the coordinates is to multiply each of the y-coordinates of the original points by the number “c”) o If 0< c < 1, c*f(x) compresses the graph of f vertically by a factor of “c” (effect on the coordinates is to multiply each of the y-coordinates of the original points by the number “c”) 1C (X) I a i x I 2: H i 2 Ix } : 1d z 'ngxl : 33 3. Reflection about the x-axis (direction of motion is vertical) 0 Multiplying f(x) by -1, -f(x), causes this reflection (effect on the coordinates is to multiply each of the y-coordinates of the original points by -l) El 1 1‘] X Transformations in the Horizontal Direction. 3}: -JT( ——.___________ . . 3| 1 x; a 1. Horizontal shifts 92 :_ (_x +2) ‘3 5 = (X ’ 3) o f(x+c) shifts the graph of f left by ‘c’ units (effect on the coordinates is to A subtract 0 from each of the X—coordinates of the original points) 0 f(x-c) shifts the graph of f right by ‘c’ units (effect on the coordinates is to mg c to each of the X-coordinates of the original points) 2. Horizontal Stretches and ShrinkingICompressions) m: (fl 0 If c > 1, f(c*x) compresses the graph of f horizontally by a factor of “c” rbalm I (effect on the coordinates is to multiply each of the x-coordinates of the [13 : 1% x} original points by the number “No” or divide them by “c”) o If 0< c < l, f(c*x) stretches the graph of f horizontally by a factor of “0” (effect on the coordinates is to multiply each of the x-coordinates of the original points by the number “l/c”) 3. Reflection about the y-axis (direction of motion is horizontal) - Substituting —x for X in f resulting in f(-x), causes this reflection (effect on the coordinates is to multiply each of the x—coordinates of the original points by - 1) ...
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This note was uploaded on 01/16/2012 for the course MATH 126 taught by Professor Blisinhestiyas during the Fall '11 term at Truckee Meadows Community College.

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1.6(one) - 1.6 Transformation of Functions.Hx I)” Library...

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