![Page 1: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/1.jpg)
Transformation of Graphs
Andrew Robertson
![Page 2: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/2.jpg)
Transformation of f(x)+a
f(x) = x2
![Page 3: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/3.jpg)
Transformation of f(x)+a
y = x2 + 3
![Page 4: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/4.jpg)
Transformation of f(x)+s
y = x2 - 2
![Page 5: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/5.jpg)
Transformation of sf(x)
f(x) = (x-2)(x-3)(x+1)
2f(x)
![Page 6: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/6.jpg)
Transformation of sf(x)
y=2f(x) = 2(x-2)(x-3)(x+1)
0.5f(x)
![Page 7: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/7.jpg)
Transformation of sf(x)
y=0.5f(x) = 0.5(x-2)(x-3)(x+1)
![Page 8: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/8.jpg)
Transformation of f(x+s)
f(x) = x2
f(x-2)
![Page 9: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/9.jpg)
Transformation of f(x+s)
y=f(x-2) = (x-2)2
f(x+2)
![Page 10: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/10.jpg)
Transformation of f(x+s)
y=f(x+2) = (x+2)2
![Page 11: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/11.jpg)
Transformation of f(sx)f(x) = (x-2)(x-3)(x+1)
f(2x)
![Page 12: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/12.jpg)
Transformation of f(sx)
y=f(2x) = (2x-2)(2x-3)(2x+1)
f(0.5x)
![Page 13: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/13.jpg)
Transformation of f(sx)
y=f(0.5x) = (0.5x-2)(0.5x-3)(0.5x+1)
-f(x)
![Page 14: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/14.jpg)
Transformation of -f(x)
f(x) = (x-2)(x-3)(x+1)
-f(x)
![Page 15: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/15.jpg)
Transformation of -f(x)
y=-f(x) = -[(x-2)(x-3)(x+1)]
f(-x)
![Page 16: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/16.jpg)
Transformation of f(-x)f(x)=(x-2)(x-3)(x+1) y=f(-x)=(-x-2)(-x-3)(-x+1)
![Page 17: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/17.jpg)
Combinations of transformations
f(x)= x2 then y=f(x+2)-3 = (x+2)2 -3
![Page 18: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/18.jpg)
Combinations of transformations
• y = x2 then y=-2f(x-3) = -2(x-3)2
![Page 19: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/19.jpg)
F(αx±β) - Inside brackets always effects the horizontal
αF(x) ±β - Outside brackets always effects the vertical
![Page 20: Transformation of Graphs Andrew Robertson. Transformation of f(x)+a f(x) = x 2](https://reader036.vdocuments.site/reader036/viewer/2022062417/551ae5e8550346b2288b659d/html5/thumbnails/20.jpg)
f(x) ± a Vertical shift (x,y) -> (x, y ± a)
f(x ± a) Horizontal shift (x,y) -> (x a, y)
Note that when + shift to Left and – shift to Right
αf(x) Vertical Stretch/compression by factor α (x,y) -> (x, αy)
f(αx) Horizontal Stretch/compression by factor 1/α
(x,y) -> (x/α, y)
f(-x) Refection though y axes (x,y) (-x, y)- f( x) Reflection through x axes (x,y) ( x, -y)