Free Printable Graph Transformations of Logarithmic Functions

1.

Logarithms and Exponentials are what?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

2.

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

a)

Horizontal shift left 5 units

b)

Horizontal shift right 5 units

c)

Vertical shift up 5 units

d)

Vertical shift down 5 units

3.

Using the parent function

y=\log_6x

what would the graph of

y=\log_6x+9

look like?

a)

Horizontal Shift to the right 9 units

b)

Horizontal shift to the left 9 units

c)

Vertical shift 9 units up

d)

Vertical shift 9 units down

4.

Describe the graph of f(x) = log x changed to

f(x) = log(x + 21) - 50

a)

translate right 21 units and 50 units down

b)

translate left 21 units and 50 units down

c)

translate right 21 units and 50 units up

d)

translate left 21 units and 50 units up

5.

What is the change in the graphs from f(x) to g(x)?

f\left(x\right)=\log_8x

to

g\left(x\right)=\log_8\left(x+9\right)-7\

a)

Right nine and down seven

b)

Left nine and down seven

c)

Left nine and up seven

d)

Right nine and up seven

6.

Describe the transformations from the parent function y=log₆x to y = - log ₆ (x - 1) - 5

a)

Reflection about the x-axis; shift left one and up five

b)

Reflection about the x-axis; shift left one and down five

c)

Reflection about the y-axis; shift right one and down five

d)

Reflection about the x-axis; shift right one and down five

7.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

8.

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

9.

What is the transformation of the logarithmic function
$f\left(x\right)=\log\ \left(x+3\right)-1$

a)

left 3, right 1

b)

right 3, down 1

c)

right 3, up 1

d)

left 3, down 1

10.

f(x)=log₅(x+4) - 2

Describe the transformation

a)

translation 4 units to the right, 2 units down

b)

translation 4 units to the left, 2 units down

c)

translation 4 units to the up, 2 units right

d)

translation 4 units to the up, 2 units left

11.

Describe the transformation on

g\left(x\right)=\log_2\left(x-3\right)

a)

The graph has been shifted 3 units up

b)

The graph has been shifted 3 units to the right

c)

The graph has been shifted 2 units right

d)

The graph has been shifted 3 units left

12.

Write the equation of the function f(x)=log(x+5)-6 after the following transformations:

Translate 3 units left and 2 units up.

a)

f(x)=log(x+2)+2

b)

f(x)=log(x+2)-4

c)

f(x)=log(x+8)-4

d)

f(x)=log(x+8)+2

13.

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

14.

Describe the transformations from the parent function $f\left(x\right)=\log_6x\ to\ g\left(x\right)=-\log_6\left(x-1\right)-5$

a)

Reflection about the x-axis; shift left one and up five

b)

Reflection about the x-axis; shift left one and down five

c)

Reflection about the y-axis; shift right one and down five

d)

Reflection about the x-axis; shift right one and down five

15.

Which graph is logarithmic

a)

b)

c)

d)

16.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

17.

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

a)

b)

c)

d)

18.

What is the range?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

19.

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

20.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

21.

What is the x-intercept of log₇(x)?

a)

(2, 0)

b)

(-1, 0)

c)

(0, 1)

d)

(1, 0)

22.

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

a)

b)

c)

d)

23.

What is the asymptote for the logarithmic function

$f\left(x\right)=\log\left(x-1\right)$

a)

x=1

b)

x=-1

c)

y=1

d)

y=-1

24.

Which graph is logarithmic

a)

b)

c)

d)

25.

Choose the equation of the graph shown.

a)

b)

c)

d)

26.

Choose the equation of the graph shown.

a)

b)

c)

d)

27.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

28.

Describe range of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

29.

Write the equation of the function f(x)=log₃x after the following transformations:

Translate 6 units left and 4 units up.

a)

g(x)=log₃(x+6)+4

b)

g(x)=log₃(x+4)-6

c)

g(x)=log₃(x-6)+4

d)

g(x)=3log(x+6)+4

30.

Find the asymptote of the following: y = log₁₀x - 6

a)

x=6

b)

x=-6

c)

x= 0

d)

y=0

31.

What is the base?

a)

1

b)

5

c)

10

d)

3

32.

What is the domain of log(x)?

a)

(-∞, ∞)

b)

[0, ∞)

c)

(0, ∞)

d)

(∞, -∞)

33.

What is the range of log(x)?

a)

(-2, 4)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

(∞, -∞)

34.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

35.

Graph $\log_7\left(x\ -\ 2\right)$

a)

b)

c)

d)

36.

graph $\log_7\left(x+2\right)+3$

a)

b)

c)

d)

37.

$g\left(x\right)=\log_3\left(x+1\right)-4$ What is the domain of the function?

a)

$\left(-4,\infty\right)$

b)

$\left(1,\infty\right)$

c)

$\left(-\infty,\infty\right)$

d)

$\left(-1,\infty\right)$

38.

What is the interval where the graph is decreasing?

f(x)=log₂(x+1)

a)

(-∞,∞)

b)

(-4,∞)

c)

(-4,9)

d)

(∞, -4)

39.

What is the interval where the graph is increasing?

f(x)=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

40.

log_a x

This function always passes thru coordinate:

a)

(0, 1)

b)

(1, 0)

c)

(0, a)

d)

(a, 0)

41.

What does K represent in this equation?

(x) = log _b(x + h) + k

a)

domain

b)

vertical shift

c)

horizontal shift

d)

base

42.

Which graph best represents the following logarithmic function?
$y=\log_2x$

a)

b)

c)

d)

Graph Transformations of Logarithmic Functions

Total questions: 42

Worksheet time: 4hrs 56mins

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