>
Precalculus>
Transformations of Functions>
Horizontal Dilations  Scale Factor (Stretch/Shrink)>
Horizontal Dilations (Stretch/Shrink) – Scale FactorHorizontal Dilations (Stretch/Shrink) – Scale Factor
Try VividMath Premium to unlock full access
Quiz summary
0 of 7 questions completed
Questions:
 1
 2
 3
 4
 5
 6
 7
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
 1
 2
 3
 4
 5
 6
 7
 Answered
 Review

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