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

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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) ...
View Full Document

## 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.

### Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online