Transformations.md

Linear Transformations of Function

$$\underset{3}{a}f(\underset{2}{b}x+\underset{1}{c})+\underset{4}{d}$$

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1. Translation c

Description

This translates the function $- c$ parallel to the $x-$axis.

Explanation

Every point on the function is moved $c$ units left.

Demonstration

<iframe scrolling="no" title="" src="https://www.geogebra.org/material/iframe/id/yxfSTZrV/width/800/height/503/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="800px" height="503px" style="border:0px;"> </iframe>

2. Dilation b

Description

This dilates the function by a scale factor $\displaystyle{\frac{1}{b}}$ parallel to the $x-$axis.

####Explanation

The distance every point on the function is from the $y-$axis is multiplied by $\displaystyle{\frac{1}{b}}$.

Demonstration

<iframe scrolling="no" title="" src="https://www.geogebra.org/material/iframe/id/t2TefJyv/width/800/height/503/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="800px" height="503px" style="border:0px;"> </iframe>

3. Dilation a

Description

This dilates the function by a scale factor $a$ parallel to the $y-$axis.

Explanation

The distance every point on the function is from the $x-$axis is multiplied by $a$.

Demonstration

<iframe scrolling="no" title="" src="https://www.geogebra.org/material/iframe/id/aQ2yGFdq/width/800/height/503/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="800px" height="503px" style="border:0px;"> </iframe>

4. Translation d

Description

This translates the function $d$ units parallel to the$y-$axis.

Explanation

Every point on the function is moved $d$ units up.

Demonstration

<iframe scrolling="no" title="" src="https://www.geogebra.org/material/iframe/id/t8v8Fsya/width/800/height/503/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="800px" height="503px" style="border:0px;"> </iframe>

General Linear Transformations Interactive

<iframe scrolling="no" title="Linear Transformations of Functions - General" src="https://www.geogebra.org/material/iframe/id/hR3ufeUF/width/800/height/503/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="800px" height="503px" style="border:0px;"> </iframe>

Linear Transformation Summary Sheet