Exponential Functions and Transformations

Exponential Functions & Transformations

Transformations

• Shifts

• Stretches

f(x) = 2^x

(Parent Function)

• g(x) = 2^x + 3 represents __________________

• h(x) = 2^x - 3 represents __________________

Domain & Range

• f(x): Domain: ___________ Range: _________

• g(x): Domain: ___________ Range: _________

• h(x): Domain: ___________ Range: _________

Multiple Choice

What is the domain of the function shown below?

• -2 < x < 5
• 0 < x < 12
• y > 0
• All Real Numbers

Multiple Choice

What is the range of the function shown below?

• 0 < y < 12
• -2 < y < 5
• y > 0
• All Real Numbers 

Multiple Choice

Which represents exponential decay?

• A

• B

• C

• D

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay

Multiple Choice

Determine the horizontal asymptote for the function

f(x) = 3(2)^x-4 + 5

• x=4

• y=4

• x=5

• y=5

Multiple Choice

Does this table represent exponential growth or decay?

• Growth

• Decay

Multiple Choice

Which function represents the table of values?

• f(x) = 4x

• f(x) = x⁴

• f(x) = 4^x

• f(x) = 4^x-1

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay

Multiple Choice

Determine the range for the function

f(x) = 3(2)^x-4 + 5

• [5,∞)

• (5,∞)

• [4,∞)

• (4,∞)

Multiple Select

Which of the following are TRUE about the function? (Choose all that apply)

• The exponential decay has been reflected.

• The exponential growth has been reflected.

• The function has been shifted down 2 units.

• The function has an growth rate of 2.

Multiple Choice

What is the a-value of the function?

• 4

• 3

• 2

• 1

Multiple Choice

Which of the following is an exponential decay? (Check all that apply)

• y = 5⋅(1/5)^x

• y = 5⋅(7/2)^x

• y = 5⋅8^x

• y = 5⋅1.5^x

Multiple Choice

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically compressed by a factor of 1/2, left 3 and down 1

• Vertically compressed by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

Multiple Choice

Which transformation is shown?

• f(x)=2^x-1-3

• f(x)=2^x-1+3

• f(x)=2^x+1-3

• f(x)=2^x+1+3

Multiple Choice

Determine the domain for the function
f(x)=3(2)^x-4+5

• [5,∞)
• (5,∞)
• (-∞,∞)
• (∞,-∞)