Single Transformations of Functions - Revision history

Khanh: /* Compressions and Stretches */

2022-01-15T18:39:54Z

Compressions and Stretches

Lila: /* Resources */

2021-10-21T20:35:01Z

Resources

Lila at 20:32, 21 October 2021

2021-10-21T20:32:02Z

Lila at 20:31, 21 October 2021

2021-10-21T20:31:19Z

Lila at 20:30, 21 October 2021

2021-10-21T20:30:17Z

Lila at 17:17, 16 September 2021

2021-09-16T17:17:12Z

Lila at 17:13, 16 September 2021

2021-09-16T17:13:40Z

Lila: /* Introduction */

2021-09-16T17:00:20Z

Introduction

Lila: /* Introduction */

2021-09-16T16:57:09Z

Introduction

Lila: /* Introduction */

2021-09-16T16:54:43Z

Introduction

@@ Line 39: / Line 39: @@
 * If <math> b > 1 </math>, then the graph will be horizontally compressed by a factor of <math> \frac{1}{b} </math>.
 * If <math> 0 < b < 1 </math>, then the graph will be horizontally stretched by a factor of <math> \frac{1}{b} </math>.
-* If b < 0, then there will be a horizontal stretch or compression of a factor of <math> |\frac{1}{b}| </math>, along with a vertical reflection.
+* If b < 0, then there will be a horizontal stretch or compression of a factor of <math> \Big|\frac{1}{b} \Big| </math>, along with a vertical reflection.
 ==Resources==

← Older revision		Revision as of 20:35, 21 October 2021
Line 43:		Line 43:
	==Resources==		==Resources==
	* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Intro to Transformations of Functions], Lumen Learning		* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Intro to Transformations of Functions], Lumen Learning
		+
		+	== Licensing ==
		+	Content obtained and/or adapted from:
		+	* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Transformations of Functions, Lumen Learning College Algebra] under a CC BY-SA license

@@ Line 2: / Line 2: @@
 <div class="floatright">
-<gallery perrow="2" widths="200px" heights="200px">
+<gallery perrow="2" widths="300px" heights="200px">
 File:Vertical shift.png|Vertical shift: <math> f(x) = x^2 </math> (red) and <math> g(x) = x^2 + 4 </math> (blue)
 File:Horizontal shift.png|Horizontal shift: <math> f(x) = sin(x) </math> (red) and <math> g(x) = sin(x + \frac{\pi}{2}) </math> (blue)

@@ Line 3: / Line 3: @@
 <div class="floatright">
 <gallery perrow="2" widths="200px" heights="200px">
-File:Vertical shift.png|thumb|Vertical shift: <math> f(x) = x^2 </math> (red) and <math> g(x) = x^2 + 4 </math> (blue)
+File:Vertical shift.png|Vertical shift: <math> f(x) = x^2 </math> (red) and <math> g(x) = x^2 + 4 </math> (blue)
-File:Horizontal shift.png|thumb|Horizontal shift: <math> f(x) = sin(x) </math> (red) and <math> g(x) = sin(x + \frac{\pi}{2}) </math> (blue)
+File:Horizontal shift.png|Horizontal shift: <math> f(x) = sin(x) </math> (red) and <math> g(x) = sin(x + \frac{\pi}{2}) </math> (blue)
-File:Vertical reflection.png|thumb|Vertical reflection: <math> f(x) = \sqrt{x} </math> (red) and <math> g(x) = -\sqrt{x} </math> (blue)
+File:Vertical reflection.png|Vertical reflection: <math> f(x) = \sqrt{x} </math> (red) and <math> g(x) = -\sqrt{x} </math> (blue)
-File:Horizontal reflection.png|thumb|Horizontal reflection: <math> f(x) = e^x </math> (red) and <math> g(x) = e^{-x} </math> (blue)
+File:Horizontal reflection.png|Horizontal reflection: <math> f(x) = e^x </math> (red) and <math> g(x) = e^{-x} </math> (blue)
-File:Vertical stretch compression.png|thumb|Vertical stretch/compression: <math> f(x) = x^2 </math> (red), <math> g(x) = \frac{1}{2}x^2 </math> (blue, vert. compression), <math> h(x) = 2x^2 </math> (green, vert. stretch), and <math> j(x) = -2x^2 </math> (black, vert. stretch and vert. reflection)
+File:Vertical stretch compression.png|Vertical stretch/compression: <math> f(x) = x^2 </math> (red), <math> g(x) = \frac{1}{2}x^2 </math> (blue, vert. compression), <math> h(x) = 2x^2 </math> (green, vert. stretch), and <math> j(x) = -2x^2 </math> (black, vert. stretch and vert. reflection)
-[[File:Horizontal stretch compression.png|thumb|Horizontal stretch/compression: <math> f(x) = \sqrt{x} </math> (red), <math> g(x) = \sqrt{2x} </math> (blue, horiz. compression), <math> h(x) = \sqrt{\frac{1}{2}x} </math> (green, horiz. stretch), and <math> j(x) = \sqrt{-2x} </math> (black, horiz. compression and horiz. reflection)
+File:Horizontal stretch compression.png|Horizontal stretch/compression: <math> f(x) = \sqrt{x} </math> (red), <math> g(x) = \sqrt{2x} </math> (blue, horiz. compression), <math> h(x) = \sqrt{\frac{1}{2}x} </math> (green, horiz. stretch), and <math> j(x) = \sqrt{-2x} </math> (black, horiz. compression and horiz. reflection)
 </gallery>
 </div>
 ===Translations===

@@ Line 1: / Line 1: @@
 ==Introduction==
 [[File:Vertical shift.png|thumb|Vertical shift: <math> f(x) = x^2 </math> (red) and <math> g(x) = x^2 + 4 </math> (blue)]]
 [[File:Horizontal shift.png|thumb|Horizontal shift: <math> f(x) = sin(x) </math> (red) and <math> g(x) = sin(x + \frac{\pi}{2}) </math> (blue)]]

← Older revision		Revision as of 17:17, 16 September 2021
Line 37:		Line 37:
	==Resources==		==Resources==
	* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Intro to Transformations of Functions], Lumen Learning		* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-transformations-of-functions/ Intro to Transformations of Functions], Lumen Learning
−	*

@@ Line 4: / Line 4: @@
 [[File:Vertical reflection.png|thumb|Vertical reflection: <math> f(x) = \sqrt{x} </math> (red) and <math> g(x) = -\sqrt{x} </math> (blue)]]
 [[File:Horizontal reflection.png|thumb|Horizontal reflection: <math> f(x) = e^x </math> (red) and <math> g(x) = e^{-x} </math> (blue)]]
-[[File:Vertical stretch compression.png|thumb|Vertical stretch/compression: <math> f(x) = x^2 </math> (red), <math> g(x) = \frac{1}{2}x^2 </math> (blue, vert. compression), <math> h(x) = 2x^2 </math> (green, vert. stretch), and <math> g(x) = -2x^2 </math> (black, vert. stretch and vert. reflection)]]
+[[File:Vertical stretch compression.png|thumb|Vertical stretch/compression: <math> f(x) = x^2 </math> (red), <math> g(x) = \frac{1}{2}x^2 </math> (blue, vert. compression), <math> h(x) = 2x^2 </math> (green, vert. stretch), and <math> j(x) = -2x^2 </math> (black, vert. stretch and vert. reflection)]]
-[[File:Horizontal stretch compression.png|thumb|Horizontal stretch/compression: <math> f(x) = \sqrt(x) </math> (red), <math> g(x) = \sqrt(2x) </math> (blue, horiz. compression), <math> h(x) = \sqrt(\frac{1}{2}x) </math> (green, horiz. stretch), and <math> g(x) = -2x^2 </math> (black, horiz. compression and horiz. reflection)]]
+[[File:Horizontal stretch compression.png|thumb|Horizontal stretch/compression: <math> f(x) = \sqrt{x} </math> (red), <math> g(x) = \sqrt{2x} </math> (blue, horiz. compression), <math> h(x) = \sqrt{\frac{1}{2}x} </math> (green, horiz. stretch), and <math> j(x) = \sqrt{-2x} </math> (black, horiz. compression and horiz. reflection)]]
 ===Translations===