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Transformations of Functions>
Combinations of Transformations: Coordinates>
Combinations of Transformations: CoordinatesCombinations of Transformations: Coordinates
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Question 1 of 3
1. Question
`(5,-2)` lies on `y=f(x)`. Find the coordinates of the image point when the function is transformed into `y=6f(x+1)+8`.
Correct
Great Work!
Incorrect
A standard function form (universal formula) for translations and dilations is `y=color(red)(k)f(color(blue)(a)(x+color(purple)(b)))+color(green)(c)` where the image point is transformed from `(color(orange)(x),color(brown)(y))` into `(color(blue)(a)(color(orange)(x)+color(purple)(b)),color(red)(k)color(brown)(y)+color(green)(c))`.To find the coordinates of the image point when the function is transformed into `y=color(red)(6)f(xcolor(purple)(+1))color(green)(+8)`, identify that `color(red)(k=6)`, `color(purple)(b=-1)`, `color(green)(c=8)`.Now transform the image point using `y=color(red)(k)f(color(blue)(a)(x+color(purple)(b)))+color(green)(c)` where the image point is transformed from `(color(orange)(x),color(brown)(y))` into `(color(blue)(a)(color(orange)(x)+color(purple)(b)),color(red)(k)color(brown)(y)+color(green)(c))`, and `(color(orange)(5),color(brown)(-2))` is the original point, `color(red)(k=6)`, `color(purple)(b=-1)`, `color(green)(c=8)`.The new image point is `(color(blue)(1)(color(orange)(5) color(purple)(-1)),(color(red)(6))(color(brown)(-2))+color(green)((8)))` which simplifies to `(4,-4)`.`(4,-4)` -
Question 2 of 3
2. Question
`(3,-2)` lies on `y=f(x)`. Find the coordinates of the image point when the function is transformed into `y=4f(-x)-9`.
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Great Work!
Incorrect
A standard function form (universal formula) for translations and dilations is `y=color(red)(k)f(color(blue)(a)(x+color(purple)(b)))+color(green)(c)` where the image point is transformed from `(color(orange)(x),color(brown)(y))` into `(color(blue)(a)(color(orange)(x)+color(purple)(b)),color(red)(k)color(brown)(y)+color(green)(c))`.To find the coordinates of the image point when the function is transformed into `y=color(red)(4)f(color(blue)(-)x)color(green)(-9)`, identify that `color(red)(k=4)`, `color(blue)(a=-1)`, `color(purple)(b=0)`, and `color(green)(c=-9)`.Now transform the image point using `y=color(red)(k)f(color(blue)(a)(x+color(purple)(b)))+color(green)(c)` where the image point is transformed from `(color(orange)(x),color(brown)(y))` into `(color(blue)(a)(color(orange)(x)+color(purple)(b)),color(red)(k)color(brown)(y)+color(green)(c))`, and `(color(orange)(3),color(brown)(-2))` is the original point, `color(red)(k=4)`, `color(blue)(a=-1)`, `color(purple)(b=0)`, and `color(green)(c=-9)`.The new image point is `(color(blue)(-1)(color(orange)(3)+color(purple)(0)),(color(red)(4))(color(brown)(-2))+color(green)((-9)))` which simplifies to `(-3,-17)`.`(-3,-17)` -
Question 3 of 3
3. Question
`(12,-1)` lies on `y=f(x)`. Find the coordinates of the image point when the function is transformed into `y=-5f(3x-6)-4`.
Correct
Great Work!
Incorrect
A standard function form (universal formula) for translations and dilations is `y=color(red)(k)f(color(blue)(a)(x+color(purple)(b)))+color(green)(c)` where the image point is transformed from `(color(orange)(x),color(brown)(y))` into `(color(blue)(a)(color(orange)(x)+color(purple)(b)),color(red)(k)color(brown)(y)+color(green)(c))`.To find the coordinates of the image point when the function is transformed into `y=color(red)(-5)f(color(blue)(3)x color(purple)(-6))color(green)(-4)`, identify that `color(red)(k=-5)`, `color(blue)(a=3)`, `color(purple)(b=-6)`, and `color(green)(c=-4)`.Now transform the image point using `y=color(red)(k)f(color(blue)(a)(x+color(purple)(b)))+color(green)(c)` where the image point is transformed from `(color(orange)(x),color(brown)(y))` into `(color(blue)(a)(color(orange)(x)+color(purple)(b)),color(red)(k)color(brown)(y)+color(green)(c))`, and `(color(orange)(12),color(brown)(-1))` is the original point, `color(red)(k=-5)`, `color(blue)(a=3)`, `color(purple)(b=-6)`, and `color(green)(c=-4)`.The new image point is `(color(blue)(-4)((color(blue)(3))(color(orange)(12))+color(purple)(-6)),(color(red)(-5))(color(brown)(-1))+color(green)((-4)))` which simplifies to `(6,1)`.`(6,1)`
Quizzes
- Vertical Translations 1
- Vertical Translations 2
- Vertical Translations from a Point
- Horizontal Translations 1
- Horizontal Translations 2
- Horizontal Translations from a Point
- Horizontal Translations from a Graph
- Horizontal and Vertical Translations from a Graph
- Sketch a Graph using Translations
- Write the Equation from a Graph
- Write the Equation from Translations
- Vertical Dilations
- Horizontal Dilations 1
- Horizontal Dilations 2
- Horizontal Dilations – Scale Factor
- Horizontal and Vertical Dilations 1
- Horizontal and Vertical Dilations 2
- Horizontal and Vertical Dilations 3
- Graphing Reflections 1
- Graphing Reflections 2
- Reflection with Rotation
- Combinations of Transformations: Order
- Combinations of Transformations: Coordinates
- Combinations of Transformations: Find Equation 1
- Combinations of Transformations: Find Equation 2
- Combinations of Transformations: Find Equation 3