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Year 12>
Transformations of Functions>
Horizontal and Vertical Dilations>
Horizontal and Vertical Dilations 3Horizontal and Vertical Dilations 3
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Question 1 of 6
1. Question
Find the transformed function from the original function `y=x^2` based on the given dilation (stretch/shrink) and scale factor.
i. Horizontally by `1/5`
ii. Vertically by `25`
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Vertical dilation takes the form `y=bb(k)f(x)` where `bb(k)` is the vertical scale factor.Horizontal dilation takes the form `y=f(color(green)(a)x)` where the scale factor can be found from `x/\text(Factor)` or `\text(Factor) =1/color(green)(a)` .i. Since the dilation (stretch/shrink) is horizontal with a factor of `1/5`, we follow the horizontal dilation form `y=f(color(green)(a)x)`.Calculate the horizontal scale factor by using `color(green)(a) =1/\text(Factor)` and `\text(Factor)=1/5`.`color(green)(a) =` `1/(1/5)` Simplify `color(green)(a)=` `5` The original function `y=x^2` will become `y=(5x)^2` or simply `y=25x^2`.ii. Since the dilation is vertical with a factor of `25`, we follow the vertical dilation form `y=(k)f(x)`. Remember that `k` is the scale factor.So, we can say the `k=25`.From there, the original function `y=x^2` will become `y=25x^2`.i. `y=25x^2` and ii. `y=25x^2` -
Question 2 of 6
2. Question
Find the transformed function from the original function `y=x^3 +4x` based on the given dilation (stretch/shrink) and scale factor.
i. Horizontally by `1/3`
ii. Vertically by `3`
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Vertical dilation takes the form `y=bb(k)f(x)` where `bb(k)` is the vertical scale factor.Horizontal dilation takes the form `y=f(color(green)(a)x)` where the scale factor can be found from `x/\text(Factor)` or `\text(Factor) =1/color(green)(a)` .i. Since the dilation (stretch/shrink) is horizontal with a factor of `1/3`, we follow the horizontal dilation form `y=f(color(green)(a)x)^2`.Calculate the horizontal scale factor by using `color(green)(a) =1/\text(Factor)` and `\text(Factor)=1/3`.`color(green)(a) =` `1/(1/3)` Simplify `color(green)(a)=` `3` The original function `y=x^3 + 4x` will become `y=(3x)^3 + 4(3x)` or simply `y=(3x)^3 + 12x`.ii. Since the dilation is vertical with a factor of `3`, we follow the vertical dilation form `y=(k)f(x)`. Remember that `k` is the scale factor.So, we can say the `k=3`.From there, the original function `y=x^3 + 4x` will become `y=3(x^3 + 4x)` or simply `y=3x^3 + 12x`.i. `y=(3x)^3 + 12x` and ii. `y=3x^3 + 12x` -
Question 3 of 6
3. Question
What dilation (stretch/shrink) is needed to transform `y=1/(x+6)` to `y=1/(4x+6)`?
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Vertical dilation takes the form `y=bb(k)f(x)` where `bb(k)` is the vertical scale factor.Horizontal dilation takes the form `y=f(color(green)(a)x)` where the scale factor can be found from `x/\text(Factor)` or `\text(Factor) =1/color(green)(a)` .To find which type of dilation (stretch/shrink) is happening, compare the transformed function `y=1/((color(green)(4)x)+6)` to the vertical dilation form `y=bb(k)f(x)` and the horizontal dilation form `y=f(color(green)(a)x)`.The transformed function `y=1/((color(green)(4)x)+6)` looks like the horizontal dilation form `y=f(color(green)(a)x)`. This means that `color(green)(a=4)`.Calculate the horizontal scale factor by using `\text(Factor) =1/color(green)(a)` and `color(green)(a=4)`.`\text(Factor) =` `1/color(green)(4)` Simplify `\text(Factor) =` `1/4` Horizontal dilation with a scale factor of `1/4` -
Question 4 of 6
4. Question
What is the equation when `y=x^2 +5` is vertically dilated (stretch/shrink) by a factor of `-1`.
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Vertical dilation takes the form `y=color(blue)(bb(k))f(x)` where `color(blue)(bb(k))` is the vertical scale factor.Horizontal dilation takes the form `y=f(ax)` where the scale factor can be found from `x/\text(Factor)` or `\text(Factor) =1/a` .Since the dilation (stretch/shrink) is vertical with a factor of `-1`, we follow the vertical dilation form `y=(k)f(x)`. Remember that `k` is the scale factor.
So, we can say the `k=-1`.From there, the original function `y=x^2 +5` will become `y=-1(x^2 +5)` or simply `y=-x^2 -5`.`y=-x^2 -5` -
Question 5 of 6
5. Question
What is the equation when `x^2 + y^2= 25` is vertically dilated (stretch/shrink) by a factor of `1/4`.
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Vertical dilation takes the form `y=color(blue)(bb(k))f(x)` where `color(blue)(bb(k))` is the vertical scale factor.Horizontal dilation takes the form `y=f(ax)` where the scale factor can be found from `x/\text(Factor)` or `\text(Factor) =1/a` .Since the dilation (stretch/shrink) is vertical with a factor of `1/4`, we follow the vertical dilation form `y=(k)f(x)`. Remember that `k` is the scale factor.
So, we can say the `k=1/4`.From there, the original function `x^2 + (y/(1/4))^2= 25` will become `x^2 + (4y)^2= 25` or simply `x^2 + 16y^2= 25`.`x^2 + 16y^2= 25` -
Question 6 of 6
6. Question
What dilation (stretch/shrink) is needed to transform `y=x^3 + 6x` to `y=1/8x^3 +3x`?
Correct
Great Work!
Incorrect
Vertical dilation takes the form `y=bb(k)f(x)` where `bb(k)` is the vertical scale factor.Horizontal dilation takes the form `y=f(color(green)(a)x)` where the scale factor can be found from `x/\text(Factor)` or `\text(Factor) =1/color(green)(a)` .To find which type of dilation (stretch/shrink) is happening, compare the transformed function `y=1/8x^3 +3x` to the vertical dilation form `y=bb(k)f(x)` and the horizontal dilation form `y=f(color(green)(a)x)`.The transformed function `y=1/8x^3 +3x` looks like the horizontal dilation form `y=f(color(green)(a)x)`. This means that `color(green)(a)=3/6` or simply `color(green)(a)=1/2`.Calculate the horizontal scale factor by using `\text(Factor) =1/color(green)(a)` and `color(green)(a=1/2)`.`\text(Factor) =` `1/color(green)(1/2)` Simplify `\text(Factor) =` `2` Horizontal dilation with a scale factor of `2`
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