7. SAS 3 Transformations

Transformations of Logs (Page 3)

Labeling

​ Page 3 #1

What is the general form of the logarithmic function?

HINT: Look in packet from two weeks ago​

Drag labels to their correct position on the image

a

k

Labeling

​ Page 3 #2

How do changes in the parameters of the general function affect the graph of the function?

HINT: Look in packet from two weeks ago​

Drag labels to their correct position on the image

stretch/ compress

no

yes

up/ down

left/ right

Categorize

Options (6)

Up 2

Down 2

Asymptote: x=0

Right 2

Left 2

Asymptote: x=2

Page 3 #3 First Box

Go to Desmos.

Type the first function in box 1.

Type the second function in box 2.

Graph on your paper.

First Function

Second Function

Both Functions

Neither Function

Categorize

Options (7)

Left 2

Right 2

Down 2

Up 2

Asymptote: x=-2

Asymptote: x=2

Asymptote: x=0

Page 3 #3 Second Box

Go to Desmos.

Type the first function in box 1.

Type the second function in box 2.

Graph on your paper.

First Function

Second Function

Neither Function

Categorize

Options (3)

Reflect across the x-axis

Stretch 2

Asymptote: x=0

Page 3 #3 Third Box

Go to Desmos.

Type the first function in box 1.

Type the second function in box 2.

Graph on your paper.

Second Function

Both Function

Multiple Select

Page 4 #4

What are the domain and range of the function $$y=3\cdot\log_2\left(x-1\right)-4$$

• Domain: All real numbers

• Range: All real numbers

• Domain: $$x>1$$

• Range: $$x>1$$

• Domain: $$x>4$$

Match

Page 4 #5

Use your knowledge of transformations of the parent function $$y=\log_2x$$ to graph the function

y = log₂(x + 2) – 4

Graph on Desmos to put on the paper. Then match below.

• a=

• h=

• k=

• Asymptote:

1

2

-4

x=-2

• 1

• 2

• -4

• x=-2

Match

Page 4 #6

Use your knowledge of transformations of the parent function $$y=\log_2x$$ to graph the function

y = 3 log₂(x - 1) – 5

Graph on Desmos to put on the paper. Then match below.

• a=

• h=

• k=

• Asymptote:

3

-1

-5

x=1

• 3

• -1

• -5

• x=1

Match

Page 5 #7

Use your knowledge of transformations of the parent function $$y=\log_{10}x$$ to graph the function

y = $$\frac{1}{2}\log_{10}\left(x\right)+4$$

Graph on Desmos to put on the paper. Then match below.

• a=

• k=

• Asymptote:

• Domain

• Range

4

x=0

x>0

All real numbers

• $$\frac{1}{2}$$

• 4

• x=0

• x>0

• All real numbers

Categorize

Options (10)

Same base of 10

Range: all real numbers

No transformations

Stretch 3

Reflect across x-axis

Right 5

Asymptote: x=0

Asymptote: x=5

Domain: x>0

Domain: x>5

Explain similarities and differences the graphs of f(x) = log₁₀(x) and g(x) = -3log₁₀(x - 5) using words like domain, range, asymptote, and transformation.

Similarities

First Function: f(x)

Second Function: g(x)