Horizontal and Vertical Dilations (Stretch/Shrink) 3

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 6

1. Question
Find the transformed function from the original function $y = x^{2}$ $y=x^2$ based on the given dilation (stretch/shrink) and scale factor.

i. Horizontally by $\frac{1}{5}$ $1/5$

ii. Vertically by $25$ $25$
- 1. i. $y = 25 x^{2}$ $y=25x^2$ and ii. $y = 25 x^{2}$ $y=25x^2$
- 2. i. $y = 25 x^{2}$ $y=25x^2$ and ii. $y = 5 x^{2}$ $y=5x^2$
- 3. i. $y = 5 x^{2}$ $y=5x^2$ and ii. $y = 25 x^{2}$ $y=25x^2$
- 4. i. $y = 5 x^{2}$ $y=5x^2$ and ii. $y = 5 x^{2}$ $y=5x^2$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Vertical dilation takes the form $y = k f (x)$ $y=bb(k)f(x)$ where $k$ $bb(k)$ is the vertical scale factor.

Horizontal dilation takes the form $y = f (a x)$ $y=f(color(green)(a)x)$ where the scale factor can be found from $\frac{x}{Factor}$ $x/\text(Factor)$ or $Factor = \frac{1}{a}$ $\text(Factor) =1/color(green)(a)$ .

i. Since the dilation (stretch/shrink) is horizontal with a factor of $\frac{1}{5}$ $1/5$ , we follow the horizontal dilation form $y = f (a x)$ $y=f(color(green)(a)x)$ .

Calculate the horizontal scale factor by using $a = \frac{1}{Factor}$ $color(green)(a) =1/\text(Factor)$ and $Factor = \frac{1}{5}$ $\text(Factor)=1/5$ .

$a =$ $color(green)(a) =$ $\frac{1}{\frac{1}{5}}$ $1/(1/5)$ Simplify

$a =$ $color(green)(a)=$ $5$ $5$

The original function $y = x^{2}$ $y=x^2$ will become $y = {(5 x)}^{2}$ $y=(5x)^2$ or simply $y = 25 x^{2}$ $y=25x^2$ .

ii. Since the dilation is vertical with a factor of $25$ $25$ , we follow the vertical dilation form $y = (k) f (x)$ $y=(k)f(x)$ . Remember that $k$ $k$ is the scale factor.

So, we can say the $k = 25$ $k=25$ .

From there, the original function $y = x^{2}$ $y=x^2$ will become $y = 25 x^{2}$ $y=25x^2$ .

i. $y = 25 x^{2}$ $y=25x^2$ and ii. $y = 25 x^{2}$ $y=25x^2$
Question 2 of 6

2. Question
Find the transformed function from the original function $y = x^{3} + 4 x$ $y=x^3 +4x$ based on the given dilation (stretch/shrink) and scale factor.

i. Horizontally by $\frac{1}{3}$ $1/3$

ii. Vertically by $3$ $3$
- 1. i. $y = 3 x^{3} + 4 x$ $y=3x^3 + 4x$ and ii. $y = {(3 x)}^{3} + 4 x$ $y=(3x)^3 + 4x$
- 2. i. $y = {(3 x)}^{3} + 12 x$ $y=(3x)^3 + 12x$ and ii. $y = 3 x^{3} + 12 x$ $y=3x^3 + 12x$
- 3. i. $y = {(3 x)}^{3} + 4 x$ $y=(3x)^3 + 4x$ and ii. $y = 3 x^{3} + 4 x$ $y=3x^3 + 4x$
- 4. i. $y = 3 x^{3} + 12 x$ $y=3x^3 + 12x$ and ii. $y = {(3 x)}^{3} + 12 x$ $y=(3x)^3 + 12x$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Vertical dilation takes the form $y = k f (x)$ $y=bb(k)f(x)$ where $k$ $bb(k)$ is the vertical scale factor.

Horizontal dilation takes the form $y = f (a x)$ $y=f(color(green)(a)x)$ where the scale factor can be found from $\frac{x}{Factor}$ $x/\text(Factor)$ or $Factor = \frac{1}{a}$ $\text(Factor) =1/color(green)(a)$ .

i. Since the dilation (stretch/shrink) is horizontal with a factor of $\frac{1}{3}$ $1/3$ , we follow the horizontal dilation form $y = {f (a x)}^{2}$ $y=f(color(green)(a)x)^2$ .

Calculate the horizontal scale factor by using $a = \frac{1}{Factor}$ $color(green)(a) =1/\text(Factor)$ and $Factor = \frac{1}{3}$ $\text(Factor)=1/3$ .

$a =$ $color(green)(a) =$ $\frac{1}{\frac{1}{3}}$ $1/(1/3)$ Simplify

$a =$ $color(green)(a)=$ $3$ $3$

The original function $y = x^{3} + 4 x$ $y=x^3 + 4x$ will become $y = {(3 x)}^{3} + 4 (3 x)$ $y=(3x)^3 + 4(3x)$ or simply $y = {(3 x)}^{3} + 12 x$ $y=(3x)^3 + 12x$ .

ii. Since the dilation is vertical with a factor of $3$ $3$ , we follow the vertical dilation form $y = (k) f (x)$ $y=(k)f(x)$ . Remember that $k$ $k$ is the scale factor.

So, we can say the $k = 3$ $k=3$ .

From there, the original function $y = x^{3} + 4 x$ $y=x^3 + 4x$ will become $y = 3 (x^{3} + 4 x)$ $y=3(x^3 + 4x)$ or simply $y = 3 x^{3} + 12 x$ $y=3x^3 + 12x$ .

i. $y = {(3 x)}^{3} + 12 x$ $y=(3x)^3 + 12x$ and ii. $y = 3 x^{3} + 12 x$ $y=3x^3 + 12x$
Question 3 of 6

3. Question
What dilation (stretch/shrink) is needed to transform $y = \frac{1}{x + 6}$ $y=1/(x+6)$ to $y = \frac{1}{4 x + 6}$ $y=1/(4x+6)$ ?
- 1. Vertical dilation with a scale factor of $4$ $4$
- 2. Horizontal dilation with a scale factor of $4$ $4$
- 3. Horizontal dilation with a scale factor of $\frac{1}{4}$ $1/4$
- 4. Vertical dilation with a scale factor of $\frac{1}{4}$ $1/4$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Vertical dilation takes the form $y = k f (x)$ $y=bb(k)f(x)$ where $k$ $bb(k)$ is the vertical scale factor.

Horizontal dilation takes the form $y = f (a x)$ $y=f(color(green)(a)x)$ where the scale factor can be found from $\frac{x}{Factor}$ $x/\text(Factor)$ or $Factor = \frac{1}{a}$ $\text(Factor) =1/color(green)(a)$ .

To find which type of dilation (stretch/shrink) is happening, compare the transformed function $y = \frac{1}{(4 x) + 6}$ $y=1/((color(green)(4)x)+6)$ to the vertical dilation form $y = k f (x)$ $y=bb(k)f(x)$ and the horizontal dilation form $y = f (a x)$ $y=f(color(green)(a)x)$ .

The transformed function $y = \frac{1}{(4 x) + 6}$ $y=1/((color(green)(4)x)+6)$ looks like the horizontal dilation form $y = f (a x)$ $y=f(color(green)(a)x)$ . This means that $a = 4$ $color(green)(a=4)$ .

Calculate the horizontal scale factor by using $Factor = \frac{1}{a}$ $\text(Factor) =1/color(green)(a)$ and $a = 4$ $color(green)(a=4)$ .

$Factor =$ $\text(Factor) =$ $\frac{1}{4}$ $1/color(green)(4)$ Simplify

$Factor =$ $\text(Factor) =$ $\frac{1}{4}$ $1/4$

Horizontal dilation with a scale factor of $\frac{1}{4}$ $1/4$
Question 4 of 6

4. Question
What is the equation when $y = x^{2} + 5$ $y=x^2 +5$ is vertically dilated (stretch/shrink) by a factor of $- 1$ $-1$ .
- 1. $y = x^{2} + 5$ $y=x^2 +5$
- 2. $y = - x^{2} + 5$ $y=-x^2 +5$
- 3. $y = x^{2} - 5$ $y=x^2 -5$
- 4. $y = - x^{2} - 5$ $y=-x^2 -5$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Vertical dilation takes the form $y = k f (x)$ $y=color(blue)(bb(k))f(x)$ where $k$ $color(blue)(bb(k))$ is the vertical scale factor.

Horizontal dilation takes the form $y = f (a x)$ $y=f(ax)$ where the scale factor can be found from $\frac{x}{Factor}$ $x/\text(Factor)$ or $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

Since the dilation (stretch/shrink) is vertical with a factor of $- 1$ $-1$ , we follow the vertical dilation form $y = (k) f (x)$ $y=(k)f(x)$ . Remember that $k$ $k$ is the scale factor.

So, we can say the $k = - 1$ $k=-1$ .

From there, the original function $y = x^{2} + 5$ $y=x^2 +5$ will become $y = - 1 (x^{2} + 5)$ $y=-1(x^2 +5)$ or simply $y = - x^{2} - 5$ $y=-x^2 -5$ .

$y = - x^{2} - 5$ $y=-x^2 -5$
Question 5 of 6

5. Question
What is the equation when $x^{2} + y^{2} = 25$ $x^2 + y^2= 25$ is vertically dilated (stretch/shrink) by a factor of $\frac{1}{4}$ $1/4$ .
- 1. $x^{2} + {(16 y)}^{2} = 25$ $x^2 + (16y)^2= 25$
- 2. ${(16 x)}^{2} + y^{2} = 25$ $(16x)^2 + y^2= 25$
- 3. $16 x^{2} + y^{2} = 25$ $16x^2 + y^2= 25$
- 4. $x^{2} + 16 y^{2} = 25$ $x^2 + 16y^2= 25$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Vertical dilation takes the form $y = k f (x)$ $y=color(blue)(bb(k))f(x)$ where $k$ $color(blue)(bb(k))$ is the vertical scale factor.

Horizontal dilation takes the form $y = f (a x)$ $y=f(ax)$ where the scale factor can be found from $\frac{x}{Factor}$ $x/\text(Factor)$ or $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

Since the dilation (stretch/shrink) is vertical with a factor of $\frac{1}{4}$ $1/4$ , we follow the vertical dilation form $y = (k) f (x)$ $y=(k)f(x)$ . Remember that $k$ $k$ is the scale factor.

So, we can say the $k = \frac{1}{4}$ $k=1/4$ .

From there, the original function $x^{2} + {(\frac{y}{\frac{1}{4}})}^{2} = 25$ $x^2 + (y/(1/4))^2= 25$ will become $x^{2} + {(4 y)}^{2} = 25$ $x^2 + (4y)^2= 25$ or simply $x^{2} + 16 y^{2} = 25$ $x^2 + 16y^2= 25$ .

$x^{2} + 16 y^{2} = 25$ $x^2 + 16y^2= 25$
Question 6 of 6

6. Question
What dilation (stretch/shrink) is needed to transform $y = x^{3} + 6 x$ $y=x^3 + 6x$ to $y = \frac{1}{8} x^{3} + 3 x$ $y=1/8x^3 +3x$ ?
- 1. Vertical dilation with a scale factor of $\frac{1}{2}$ $1/2$
- 2. Horizontal dilation with a scale factor of $\frac{1}{2}$ $1/2$
- 3. Horizontal dilation with a scale factor of $2$ $2$
- 4. Vertical dilation with a scale factor of $2$ $2$
Correct

Great Work!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

Vertical dilation takes the form $y = k f (x)$ $y=bb(k)f(x)$ where $k$ $bb(k)$ is the vertical scale factor.

Horizontal dilation takes the form $y = f (a x)$ $y=f(color(green)(a)x)$ where the scale factor can be found from $\frac{x}{Factor}$ $x/\text(Factor)$ or $Factor = \frac{1}{a}$ $\text(Factor) =1/color(green)(a)$ .

To find which type of dilation (stretch/shrink) is happening, compare the transformed function $y = \frac{1}{8} x^{3} + 3 x$ $y=1/8x^3 +3x$ to the vertical dilation form $y = k f (x)$ $y=bb(k)f(x)$ and the horizontal dilation form $y = f (a x)$ $y=f(color(green)(a)x)$ .

The transformed function $y = \frac{1}{8} x^{3} + 3 x$ $y=1/8x^3 +3x$ looks like the horizontal dilation form $y = f (a x)$ $y=f(color(green)(a)x)$ . This means that $a = \frac{3}{6}$ $color(green)(a)=3/6$ or simply $a = \frac{1}{2}$ $color(green)(a)=1/2$ .

Calculate the horizontal scale factor by using $Factor = \frac{1}{a}$ $\text(Factor) =1/color(green)(a)$ and $a = \frac{1}{2}$ $color(green)(a=1/2)$ .

$Factor =$ $\text(Factor) =$ $\frac{1}{\frac{1}{2}}$ $1/color(green)(1/2)$ Simplify

$Factor =$ $\text(Factor) =$ $2$ $2$

Horizontal dilation with a scale factor of $2$ $2$

Horizontal and Vertical Dilations (Stretch/Shrink) 3

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Great Work!

2. Question

Great Work!

3. Question

Great Work!

4. Question

Great Work!

5. Question

Great Work!

6. Question

Great Work!

Quizzes

$a =$ $color(green)(a) =$		$\frac{1}{\frac{1}{5}}$ $1/(1/5)$	Simplify
$a =$ $color(green)(a)=$		$5$ $5$

$a =$ $color(green)(a) =$		$\frac{1}{\frac{1}{3}}$ $1/(1/3)$	Simplify
$a =$ $color(green)(a)=$		$3$ $3$

$Factor =$ $\text(Factor) =$		$\frac{1}{4}$ $1/color(green)(4)$	Simplify
$Factor =$ $\text(Factor) =$		$\frac{1}{4}$ $1/4$

$Factor =$ $\text(Factor) =$		$\frac{1}{\frac{1}{2}}$ $1/color(green)(1/2)$	Simplify
$Factor =$ $\text(Factor) =$		$2$ $2$