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Transformations of Functions>
Horizontal and Vertical Dilations (Stretch/Shrink)>
Horizontal and Vertical Dilations (Stretch/Shrink) 2Horizontal and Vertical Dilations (Stretch/Shrink) 2
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Question 1 of 6
1. Question
Describe if the constant in the transformed function shows a horizontal or vertical dilation (stretch/shrink) and state the scale factor.
Original function `y=x^2`
Transformed function `y=(x/3)^2`
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=(color(green)(1/3)x)^2` 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=(color(green)(1/3)x)^2` looks like the horizontal dilation form `y=f(color(green)(a)x)`. This means that `color(green)(a=1/3)`.Calculate the horizontal scale factor by using `\text(Factor) =1/color(green)(a)` and `color(green)(a=1/3)`.`\text(Factor) =` `1/color(green)(1/3)` Simplify `\text(Factor) =` `3` Horizontal dilation with a scale factor of `3` -
Question 2 of 6
2. Question
Describe if the constant in the transformed function shows a horizontal or vertical dilation (stretch/shrink) and state the scale factor.
Original function `y=x^4`
Transformed function `y=x^4/6`
Correct
Great Work!
Incorrect
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` .To find which type of dilation (stretch/shrink) is happening compare the transformed function `y=color(blue)(bb(1/6))x^4` to the vertical dilation form `y=color(blue)(bb(k))f(x)` and the horizontal dilation form `y=f(ax)`.The transformed function `y=color(blue)(bb(1/6))x^4` looks like the vertical dilation form `y=color(blue)(bb(k))f(x)`. This means that `color(blue)(k=1/6)`. Remember `k` is the scale factor.Vertical dilation with a scale factor of `1/6` -
Question 3 of 6
3. Question
Describe if the constant in the transformed function shows a horizontal or vertical dilation (stretch/shrink) and state the scale factor.
Original function `y=x^3`
Transformed function `y=5x^3`
Correct
Great Work!
Incorrect
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` .To find which type of dilation (stretch/shrink) is happening compare the transformed function `y=color(blue)(bb(5))x^3` to the vertical dilation form `y=color(blue)(bb(k))f(x)` and the horizontal dilation form `y=f(ax)`.The transformed function `y=color(blue)(bb(5))x^3` looks like the vertical dilation form `y=color(blue)(bb(k))f(x)`. This means that `color(blue)(k=5)`. Remember `k` is the scale factor.Vertical dilation with a scale factor of `5` -
Question 4 of 6
4. Question
Describe if the constant in the transformed function shows a horizontal or vertical dilation (stretch/shrink) and state the scale factor.
Original function `y=3^x`
Transformed function `y=3^(1/2 x)`
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=3^(color(green)(1/2)x)` 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=3^(color(green)(1/2)x)` looks like the horizontal dilation form `y=f(color(green)(a)x)`. This means that `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` -
Question 5 of 6
5. Question
Describe if the constant in the transformed function shows a horizontal or vertical dilation (stretch/shrink) and state the scale factor.
Original function `y=e^x`
Transformed function `y=e^x /3`
Correct
Great Work!
Incorrect
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` .To find which type of dilation (stretch/shrink) is happening compare the transformed function `y=color(blue)(bb(1/3))e^x` to the vertical dilation form `y=color(blue)(bb(k))f(x)` and the horizontal dilation form `y=f(ax)`.The transformed function `y=color(blue)(bb(1/3))e^x` looks like the vertical dilation form `y=color(blue)(bb(k))f(x)`. This means that `color(blue)(k=1/3)`. Remember `k` is the scale factor.Vertical dilation with a scale factor of `1/3` -
Question 6 of 6
6. Question
Describe if the constant in the transformed function shows a horizontal or vertical dilation (stretch/shrink) and state the scale factor.
Original function `y=\log(x)`
Transformed function `y=4\log(x)`
Correct
Great Work!
Incorrect
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` .To find which type of dilation (stretch/shrink) is happening compare the transformed function `y=color(blue)(bb(4))\log(x)` to the vertical dilation form `y=color(blue)(bb(k))f(x)` and the horizontal dilation form `y=f(ax)`.The transformed function `y=color(blue)(bb(4))\log(x)` looks like the vertical dilation form `y=color(blue)(bb(k))f(x)`. This means that `color(blue)(k=4)`. Remember `k` is the scale factor.Vertical dilation with a scale factor of `4`
Quizzes
- Vertical Translations (Shifts) 1
- Vertical Translations (Shifts) 2
- Vertical Translations (Shifts) from a Point
- Horizontal Translations (Shifts) 1
- Horizontal Translations (Shifts) from a Point
- Horizontal Translations (Shifts) from a Graph
- Horizontal and Verticals Translations (Shifts) from a Graph
- Sketch a Graph using Translations (Shifts)
- Write the Equation from a Graph
- Write the Equation from Translations (Shifts) 1
- Vertical Dilations (Stretch/Shrink)
- Horizontal Dilations (Stretch/Shrink) 1
- Horizontal Dilations (Stretch/Shrink) 2
- Horizontal Dilations (Stretch/Shrink) – Scale Factor
- Horizontal and Vertical Dilations (Stretch/Shrink) 1
- Horizontal and Vertical Dilations (Stretch/Shrink) 2
- Horizontal and Vertical Dilations (Stretch/Shrink) 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