Horizontal and Vertical Dilations (Stretch/Shrink) 1

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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 $y=(5x)^2$
- 1. Vertical dilation with a scale factor of $5$
- 2. Vertical dilation with a scale factor of $1/5$
- 3. Horizontal dilation with a scale factor of $5$
- 4. Horizontal dilation with a scale factor of $1/5$
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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 $y=(color(green)(5)x)^2$ to the vertical dilation form $y=bb(k)f(x)$ and the horizontal dilation form $y=f(color(green)(a)x)$ .

The transformed function $y=(color(green)(5)x)^2$ looks like the horizontal dilation form $y=f(color(green)(a)x)$ . This means that $color(green)(a=5)$ .

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

$\text(Factor) =$ $1/color(green)(5)$ Simplify

$\text(Factor) =$ $1/5$

Horizontal dilation with a scale factor of $1/5$
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 $y=x^2$

Transformed function $y=(-x)^2$
- 1. Vertical dilation with a scale factor of $-1$
- 2. Vertical dilation with a scale factor of $1$
- 3. Horizontal dilation with a scale factor of $1$
- 4. Horizontal dilation with a scale factor of $-1$
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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 $y=(color(green)(-1)x)^2$ to the vertical dilation form $y=bb(k)f(x)$ and the horizontal dilation form $y=f(color(green)(a)x)$ .

The transformed function $y=(color(green)(-1)x)^2$ looks like the horizontal dilation form $y=f(color(green)(a)x)$ . This means that $color(green)(a=-1)$ .

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

$\text(Factor) =$ $1/color(green)(-1)$ Simplify

$\text(Factor) =$ $-1$

Horizontal dilation with a scale factor of $-1$
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 $y=x^4$

Transformed function $y=(4x)^4$
- 1. Horizontal dilation with a scale factor of $1/4$
- 2. Horizontal dilation with a scale factor of $4$
- 3. Vertical dilation with a scale factor of $1/4$
- 4. Vertical dilation with a scale factor of $4$
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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 $y=(color(green)(4)x)^4$ to the vertical dilation form $y=bb(k)f(x)$ and the horizontal dilation form $y=f(color(green)(a)x)$ .

The transformed function $y=(color(green)(4)x)^4$ 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
Describe if the constant in the transformed function shows a horizontal or vertical dilation and state the scale factor.

Original function $y=x^3$

Transformed function $y=(2x)^3$
- 1. Horizontal dilation with a scale factor of $1/2$
- 2. Horizontal dilation with a scale factor of $2$
- 3. Vertical dilation with a scale factor of $1/2$
- 4. Vertical dilation with a scale factor of $2$
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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 is happening compare the transformed function $y=(color(green)(2)x)^3$ to the vertical dilation form $y=bb(k)f(x)$ and the horizontal dilation form $y=f(color(green)(a)x)$ .

The transformed function $y=(color(green)(2)x)^3$ looks like the horizontal dilation form $y=f(color(green)(a)x)$ . This means that $color(green)(a=2)$ .

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

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

$\text(Factor) =$ $1/2$

Horizontal dilation with a scale factor of $1/2$
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 $y=2^x$

Transformed function $y=-2^x$
- 1. Horizontal dilation with a scale factor of $-1$
- 2. Vertical dilation with a scale factor of $-1$
- 3. Horizontal dilation with a scale factor of $1$
- 4. Vertical dilation with a scale 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 $\text(Factor) =1/a$ .

To find which type of dilation (stretch/shrink) is happening compare the transformed function $y=color(blue)(bb(-1))*2^x$ to the vertical dilation form $y=color(blue)(bb(k))f(x)$ and the horizontal dilation form $y=f(ax)$ .

The transformed function $y=color(blue)(bb(-1))*2^x$ looks like the vertical dilation form $y=color(blue)(bb(k))f(x)$ . This means that $color(blue)(k=-1)$ . Remember $k$ is the scale factor.

Vertical dilation with a scale factor of $-1$
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 $y=4\log(x)$
- 1. Horizontal dilation with a scale factor of $4$
- 2. Horizontal dilation with a scale factor of $1/4$
- 3. Vertical dilation with a scale factor of $4$
- 4. Vertical dilation with a scale 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 $\text(Factor) =1/a$ .

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 $4$

Horizontal and Vertical Dilations (Stretch/Shrink) 1

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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6. Question

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Quizzes

$\text(Factor) =$		$1/color(green)(5)$	Simplify
$\text(Factor) =$		$1/5$

$\text(Factor) =$		$1/color(green)(-1)$	Simplify
$\text(Factor) =$		$-1$

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

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