Wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Transformation of the Graph of Logarithmic Function

Total questions: 22

Worksheet time: 17mins

Name
Class
Date
1.
Determine the order of transformations
a)
left 1, reflected over x-axis
b)
up 1, reflected over y-axis
c)
right 1, reflected over x-axis
d)
left 1, reflected over y-axis
2.

Select all the transformations that apply.

y = log 6 (x - 1) - 5

a)

Horizontal shift left 1

b)

Horizontal shift right 1

c)

Vertical shift up 5

d)

Vertical shift down 5

3.

Select all the transformations that apply.

y = log 5 (x + 1) +1

a)

Horizontal shift left 1

b)

Horizontal shift right 1

c)

Vertical shift up 1

d)

Vertical shift down 1

4.

Select all the transformations that apply.

y = -2 log 1/2 x

a)

Vertical stretch by 2

b)

Vertical shrink by 1/2

c)

Reflection across the y-axis

d)

Reflection across the x-axis

5.

Select all the transformations that apply.

y = 3log 3 (2x)

a)

Vertical stretch by 3

b)

Vertical shrink by 1/3

c)

Horizontal shrink by 1/2

d)

Horizontal stretch by 2

6.
In the general log function 
y = a*logb(x-h)+k, what letter tells us if the function has moved left or right?
a)
a
b)
b
c)
h
d)
k
7.

What transformation is occurring vertically? y = 2/3 log x

a)

stretch

b)

compression

8.

What transformation is occurring? y = log x - 6

a)

Horizontal shift left 6

b)

Horizontal shift right 6

c)

Vertical shift up 6

d)

Vertical shift down 6

9.
find the asymptote: y = log10 (x+3)
a)
x=-3
b)
x=3
c)
y=-3
d)
y=3
10.
Find the asymptote of the following: y = log10 x - 6
a)
x=6
b)
x=-6
c)
x= 0
d)
y=0
11.

What is the asymptote of y = log2x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

12.

The asymptote of y = log2x + 1 will shift...

a)

right one to x = 1

b)

left one to x = -1

c)

not shift at all and remain x = 0

13.
Classify the following graph.
a)
Exponential Growth
b)
Exponential Decay
c)
Logarithmic
14.
Which has a vertical asymptote?
a)
Exponential
b)
Logarithmic
c)
Both
15.
Which has a horizontal asymptote?
a)
Exponential
b)
Logarithmic
c)
Both
16.
What is the equation of the asymptote?
a)
x = -3
b)
x=5
c)
y= -3
d)
y=5
17.
What are the transformations of this graph?
a)
Right 1 Up 5
b)
Right 1 Down 5
c)
Left 1 Up 5
d)
Left 1 Down 5
18.
What is the parent function seen here?
a)
Logarithmic
b)
Exponential
c)
Square Root
d)
Constant Function
19.

Describe the transformations of f(x)= -log2(x+1)

a)

left one & y-axis reflection

b)

right one & y-axis reflection

c)

left one & x-axis reflection

d)

right one & x-axis reflection

20.
Match the graph with its equation
a)
y = log6(-x) + 1
b)
y = log6(x − 2) + 1
c)
y = log6(x + 2) - 1
d)
y = log(x-8) + 1
21.
Match the graph with its equation
a)
y = log5 (x + 1) + 1 
b)
y = log5 (x - 1) + 1 
c)
y = log5 (x2) + 1 
d)
y = log5 (x)-1
22.
Match the graph with its equation
a)
y = log4 (x)+2
b)
y = log4 (x + 2) + 1 
c)
y = log4 (x - 1) + 2
d)
y = log4 (-x + 2)