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Horizontal Dilations - Scale Factor (Stretch/Shrink)>
Horizontal Dilations (Stretch/Shrink) – Scale FactorHorizontal Dilations (Stretch/Shrink) – Scale Factor
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Question 1 of 7
1. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `4` to the function `y=2^x`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilations (stretch/shrink) of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ \ \ \ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation (stretch/shrink), first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=4)`. Factor of `4` means it is stretched `4` times as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/color(red)(4)`.`y=` `2^(color(blue)(1/4)\timesx)` Write the new equation using `y=2^(color(blue)(a)x)` and `color(blue)(a=1/4)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `2^(x/4)` `y=2^(x/4)` -
Question 2 of 7
2. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `1/2` to the function `y=sqrt(x)`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilations (stretch/shrink) of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation (stretch/shrink), first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=1/2)`. Factor of `1/2` means it is compressed half as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/(color(red)(1/2))=2`.`y=` `sqrt(color(blue)(2)\timesx)` Write the new equation using `y=sqrt(color(blue)(a)x)` and `color(blue)(a=2)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `sqrt(2x)` `y=sqrt(2x)` -
Question 3 of 7
3. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `1/2` to the function `y=2^x`.
Correct
Great Work!
Incorrect
Horizontal dilations of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation, first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=1/2)`. Factor of `1/2` means it is compressed half as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/(color(red)(1/2))=2`.`y=` `2^(color(blue)(2)\timesx)` Write the new equation using `y=2^(color(blue)(a)x)` and `color(blue)(a=2)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `2^(2x)` `y=2^(2x)` -
Question 4 of 7
4. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `3` to the function `y=x^3`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilations (stretch/shrink) of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation (stretch/shrink), first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=3)`. Factor of `3` means it is stretched `3` times as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/(color(red)(3)`.`y=` `(color(blue)(1/3)\timesx)^3` Write the new equation using `y=(color(blue)(a)x)^3` and `color(blue)(a=1/3)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `(x/3)^3` `y=(x/3)^3` -
Question 5 of 7
5. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `6` to the function `y=log(x)`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilations (stretch/shrink) of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation (stretch/shrink), first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=6)`. Factor of `6` means it is stretched `6` times as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/color(red)(6)`.`y=` `log(color(blue)(1/6 )\timesx)` Write the new equation using `y=log(color(blue)(a)x)` and `color(blue)(a=1/6)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `log(x/6)` `y=log(x/6)` -
Question 6 of 7
6. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `1/8` to the function `y=log(x)`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilations (stretch/shrink) of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation (stretch/shrink), first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=1/8)`. Factor of `1/8` means it is compressed `1/8` as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/(color(red)(1/8))=8`.`y=` `log(color(blue)(8)\timesx)` Write the new equation using `y=log(color(blue)(a)x)` and `color(blue)(a=8)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `log(8x)` `y=log(8x)` -
Question 7 of 7
7. Question
Apply the horizontal dilation (stretch/shrink) scale factor of `4` to the function `y=x^2`.
Correct
Great Work!
Incorrect
A Dilation is to stretch or to shrink the shape of a curve.
Horizontal dilations (stretch/shrink) of a function are written in the form `y=f(ax)`. To find `color(blue)(a)`, use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))` or `color(red)(\text(Factor))=1/color(blue)(a)`.Alternatively, we can take the `x` component of the function and divide it by the horizontal dilation factor: `\ \ x/color(red)(\text(Factor))`To obtain the equation of the function after the horizontal dilation (stretch/shrink), first solve for `color(blue)(a)` where the `color(red)(\text(Factor)=4)`. Factor of `4` means it is stretched `4` times as wide horizontally. Use the formula `color(blue)(a)=1/(color(red)(\text(Factor)))`.This gives `color(blue)(a)=1/(color(red)(\text(Factor)))=1/color(red)(4)`.`y=` `(color(blue)(1/4)\timesx)^2` Write the new equation using `y=(color(blue)(a)x)^2` and `color(blue)(a=1/4)`. Remember horizontal dilations of a function are written in the form `y=f(color(blue)(a)x)`. `y=` `(x/4)^2` `y=(x/4)^2`
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