Describe the transformations in the logarithmic function y = 4 log ⁡ 3 x + 7 y=4\log_3x\ +7 y = 4 lo g 3 x + 7

vertical stretch by 4, up 7 units

vertical compression by 4, left 7 units

Describe the transformations in the logarithmic function y = − log ⁡ ( x − 5 ) y=-\ \log_{ }\left(x-5\right) y = − lo g ( x − 5 )

reflection over the x-axis, right 5 units

reflection over the x-axis, left 5 units

vertical compression, down 5 units

Find the domain and range of: f(x) = log 2 (x)

Domain: x > 0 Range: all real numbers

Domain: all real numbers Range: all real numbers

Domain: all real numbers Range: y < 0

The asymptote of y = log 2 x + 9 will shift...

not shift at all and remain x = 0

Describe the graph of f(x) = log x changed to f(x) = log(x + 21) - 50

translate left 21 units and 50 units down

translate right 21 units and 50 units down

translate right 21 units and 50 units up

translate left 21 units and 50 units up

Transformations of logarithmic functions

Authored by Nicholas Steinkemper

Mathematics

10th - 11th Grade

CCSS covered

Used 179+ times

Transformations of logarithmic functions

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25 questions

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MULTIPLE CHOICE QUESTION

1 min • 12 pts

Which graph best represents the following logarithmic function?
$y=\log_4x$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which type of function has a horizontal asymptote?

exponential

logarithm

both

neither

Tags

CCSS.HSF-IF.C.7D

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which type of function has a vertical asymptote?

exponential

logarithm

both

neither

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 12 pts

Where is the asymptote?

x = 1

y = 1

x = -1

y = -1

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the domain?

$x>1$

$x<1$

$y>1$

$y<1$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the range?

All real numbers

$x>1$

$y<2$

$y>1$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Using the parent function $y=\log_3x$ what would the graph of $y=\log_3\left(x+5\right)$ look like?

Horizontal shift left 5 units

Horizontal shift right 5 units

Vertical shift up 5 units

Vertical shift down 5 units

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Using the parent function
$y=\log_3x$ what would the graph of $y=\log_3x+5$ look like?

Horizontal Shift to the right 5 units

Horizontal shift to the left 5 units

Vertical shift 5 units up

Vertical shift 5 units down

Tags

CCSS.HSF-IF.C.7E

10.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What are the transformations of this function?
$y=\frac{1}{3}\log_2x-8$

vertical compression by 1/3, down 8

vertical stretch by 1/3, down 8

vertical compression by 1/3, right 8

reflection across the x-axis, right 8

Tags

CCSS.HSF.BF.B.3

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Transformations of logarithmic functions

Which graph best represents the following logarithmic function? y=log⁡4xy=\log_4xy=log4​x

Which type of function has a horizontal asymptote?

Which type of function has a vertical asymptote?

Where is the asymptote?

What is the domain?

What is the range?

Using the parent function y=log⁡3xy=\log_3xy=log3​x what would the graph of y=log⁡3(x+5)y=\log_3\left(x+5\right)y=log3​(x+5) look like?

Using the parent function y=\log_3xy=log3​x what would the graph of y=log⁡3x+5y=\log_3x+5y=log3​x+5 look like?

What is the Vertical Asymptote?

What are the transformations of this function? y=13log⁡2x−8y=\frac{1}{3}\log_2x-8y=31​log2​x−8

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Which graph best represents the following logarithmic function?
$y=\log_4x$

Using the parent function $y=\log_3x$ what would the graph of $y=\log_3\left(x+5\right)$ look like?

Using the parent function
$y=\log_3x$ what would the graph of $y=\log_3x+5$ look like?

What are the transformations of this function?
$y=\frac{1}{3}\log_2x-8$