Horizontal and Vertical Dilations 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 $y = x^{2}$ $y=x^2$

Transformed function $y = {(\frac{x}{3})}^{2}$ $y=(x/3)^2$
- 1. Vertical dilation with a scale factor of $\frac{1}{3}$ $1/3$
- 2. Vertical dilation with a scale factor of $3$ $3$
- 3. Horizontal dilation with a scale factor of $3$ $3$
- 4. Horizontal dilation with a scale factor of $\frac{1}{3}$ $1/3$
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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 $y = {(\frac{1}{3} x)}^{2}$ $y=(color(green)(1/3)x)^2$ 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 $y = {(\frac{1}{3} x)}^{2}$ $y=(color(green)(1/3)x)^2$ looks like the horizontal dilation form $y = f (a x)$ $y=f(color(green)(a)x)$ . This means that $a = \frac{1}{3}$ $color(green)(a=1/3)$ .

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

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

$Factor =$ $\text(Factor) =$ $3$ $3$

Horizontal dilation with a scale factor of $3$ $3$
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 $y = x^{4}$ $y=x^4$

Transformed function $y = \frac{x^{4}}{6}$ $y=x^4/6$
- 1. Horizontal dilation with a scale factor of $6$ $6$
- 2. Vertical dilation with a scale factor of $6$ $6$
- 3. Horizontal dilation with a scale factor of $\frac{1}{6}$ $1/6$
- 4. Vertical dilation with a scale factor of $\frac{1}{6}$ $1/6$
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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 $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

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

The transformed function $y = \frac{1}{6} x^{4}$ $y=color(blue)(bb(1/6))x^4$ looks like the vertical dilation form $y = k f (x)$ $y=color(blue)(bb(k))f(x)$ . This means that $k = \frac{1}{6}$ $color(blue)(k=1/6)$ . Remember $k$ $k$ is the scale factor.

Vertical dilation with a scale factor of $\frac{1}{6}$ $1/6$
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 $y = x^{3}$ $y=x^3$

Transformed function $y = 5 x^{3}$ $y=5x^3$
- 1. Vertical dilation with a scale factor of $\frac{1}{5}$ $1/5$
- 2. Horizontal dilation with a scale factor of $5$ $5$
- 3. Vertical dilation with a scale factor of $5$ $5$
- 4. Horizontal dilation with a scale factor of $\frac{1}{5}$ $1/5$
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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 $Factor = \frac{1}{a}$ $\text(Factor) =1/a$ .

To find which type of dilation (stretch/shrink) is happening compare the transformed function $y = 5 x^{3}$ $y=color(blue)(bb(5))x^3$ to the vertical dilation form $y = k f (x)$ $y=color(blue)(bb(k))f(x)$ and the horizontal dilation form $y = f (a x)$ $y=f(ax)$ .

The transformed function $y = 5 x^{3}$ $y=color(blue)(bb(5))x^3$ 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 $y=3^(1/2 x)$
- 1. Vertical dilation with a scale factor of $2$
- 2. Vertical dilation with a scale factor of $1/2$
- 3. Horizontal dilation with a scale factor of $1/2$
- 4. Horizontal 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 (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 $y=e^x /3$
- 1. Vertical dilation with a scale factor of $3$
- 2. Horizontal dilation with a scale factor of $1/3$
- 3. Vertical dilation with a scale factor of $1/3$
- 4. Horizontal dilation with a scale factor of $3$
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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 $y=color(blue)(bb(1/3))e^x$ 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 $y=4\log(x)$
- 1. Vertical dilation with a scale factor of $1/4$
- 2. Horizontal dilation with a scale factor of $4$
- 3. Horizontal 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 $y=color(blue)(bb(k))f(x)$ 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 2

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6. Question

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Quizzes

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

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