Graphs of Exponential/Logarithmic functions

Transformations of Functions

100

Describe the transformations

f(x)=2^x + 4

What is 

Translated 4 units up 

200

Describe the transformation(s) 

f(x)=4^x - 3 

What is 

Translated down 3 units 

300

Describe the transformation(s) 

f(x)= 5 ^x-4 - 4

What is

Translated right 4 units 

Translated down 4 units 

400

Describe the transformation(s) 

f(x)=log₃ (x+2) - 7

What is 

Translated left 2 units

Translated down 7 units

500

Describe the transformation(s) 

f(x)= -2log₃ (x-6) + 1

What is

Vertical reflection over x-axis 

Vertical stretch by a factor of 2 

Translated right 6 units

Translated up 1 unit

Graphing exponential and logarithmic functions

100

What are the two original points? 

f(x) = log₃ x

(1,0 ) and (3,1) 

200

What are the two original points of the graph 

f(x)=4^x

What is 

(0,1) and (1,4) 

300

What are the two original points and their shifted points? 

f(x)=log₃ (x+2)

What is 

( 1, 0) -> (-1, 0) 

(3, 1) -> (1, 1)

400

What are the two original points and their shifted ones for the graph 

f(x) =2 log₂(x) - 1  

What is

(1, 0) -> (1,-1)

(2,2) -> (2, 1)

500

What are the two original points and their shifted ones for the graph of 

f(x)=3log₂ (x-3) - 3

What is

(1, 0 ) -> (4, -3)

(2, 3) -> (5, 0)

Characteristics of Exponential Function graphs

100

Find the domain and range of 

f(x)=4^x

What is

Domain: (-∞, ∞)

Range: (0, ∞)

200

Find the domain and range of 

f(x) = 5^x+2

What is

domain: (-∞, ∞)

range: (2, ∞)

300

Find the interval of increase/decrease of 

f(x)=4^x

What is

Interval of increase: (-∞, ∞)

Interval of decrease: N/A 

400

Find the positive and negative interval of 

f(x)=2^x

What is 

positive interval: (-∞, ∞)

negative interval: N/A 

500

What is the end behavior of 

f(x)=(1/2)^x

What is 

as x -> -∞, f(x) -> ∞

as x -> ∞, f(x) -> 0

Characteristics of Logarithmic Function graphs

100

Find the domain and range of 

f(x)=log₂ x

what is 

Domain: (0, ∞) 

range: (-∞, ∞)

200

Find the domain and range of 

f(x)=log₂ (x+1)

Domain: (-1, ∞) 

range: (-∞, ∞)

300

Find the interval of increase/decrease of 

f(x)=log₃x

What is 

interval of increase: (0, ∞) 

interval of decrease: N/A 

400

Find the end-behavior of 

f(x)=log₅ x

what is 

as x -> 0, f(x) -> -∞

as x -> ∞, f(x) -> ∞

500

What is the end behavior of 

f(x)= log₃ (x+2)

what is 

as x -> -2, f(x) -> -∞

as x -> ∞, f(x) -> ∞

Asymptotes

100

An exponential function has a ________ asymptote. 

What is 

horizontal 

200

A logarithmic function has a ___________ asymptote. 

What is 

vertical 

300

Find the asymptote of 

f(x)=4^x - 3 

What is 

y=-3 

400

Find the asymptote of 

f(x)=log₂(x+3)-2 

What is 

x=-3 

500

Find the asymptotes of 

f(x)=log₃ (x-2) + 5 

What is 

x=2