Exponential Functions Review

Exponential Functions

Exponential Functions have a variable in the exponent

Remember

Linear functions have a constant rate of change (as x increases, y increases by constant addition or subtraction.

Exponential functions have a constant multiplier (as x increases, y increases by multiplication).

​Examples

Non Examples

​Exponential Functions

Multiple Choice

What is b-value in this function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

Multiple Choice

How do you know that this is exponential growth? $$f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$$  

• Because the 0.25 was bigger than one

• Because the 1.3 was bigger than one

• Because the 0.25 was less than one

• Because the 1.3 was less than one

Multiple Choice

How do you know that this is exponential decay? $$f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$$  

• Because the 25 was bigger than one

• Because the 0.20 was bigger than one

• Because the 25 was less than one

• Because the 0.20 was less than one

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Multiple Select

Which of the following are exponential functions?

• f(x)=4(2)^x

• y=4x²

• y=5^x

• f(x)=3x⁴

Exponential Functions

f(x) = a (b)^x

^{a = initial value or starting amount}

^{b= (common ratio) growth or decay factor}

Multiple Choice

What is the initial value in y=4(2)^x

• 4

• 2

• x

Multiple Choice

What is the y-intercept in y=4(2)^x

• (4,0)

• (0,2)

• x

• (0,4)

• (4,2)

Multiple Choice

What is the y-intercept of f(x)=5(3)^x

• (0,5)

• (0,3)

• (3,0)

• (5,0)

Multiple Choice

What is the starting amount in the problem below?

f(t) = 300(1.05)^t

• 300

• 1.05

• t

• y

Multiple Choice

What is the growth rate in the problem below?

f(t) = 300(1.05)^t

• 300

• 1.05

• t

• y

Multiple Choice

What is the common ratio for the function f(x) = 25 (4)^x

• 25

• 4

Exponential

Growth vs. Decay

If b > 1 then Growth

If b is a fraction

0

Both Graphs have a

Horizontal Asymptote

(graph never touches

the X-axis)

b^x cannot equal 0

Multiple Choice

b⁰ =

• -1

• 0

• 1

Multiple Choice

The y-intercept for any function in the form

y=b^x

• (0,0)

• (0,1)

• (1,0)

Multiple Choice

The y-intercept for any function in the form

y=b^x

• (0,0)

• (0,1)

• (1,0)

Transformations

• Shifts

• Stretches

f(x) = 2^x

(Parent Function)

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

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

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

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

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