G11 Les 5.1 Graphing Exponential functions

Exponential Functions

f(x) = a (b)^x

^{a = initial value or starting amount}

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

Exponential Functions have a variable in the exponent

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Multiple Choice

In an exponential function, what does the 'a' represent?

• SLOPE

• RATE OF CHANGE

• Y-INTERCEPT

• COMMON RATIO

Multiple Choice

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

• (.27)^x
• .27
• 13
• 3.51

Multiple Choice

What is the y-intercept of the function?

• 2
• 3
• 1
• -2

Multiple Choice

What is the x-intercept of the exponential function? 

• (0,1)
• (0,0)
• There is not one

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

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x
• y = 50x - 4
• y = (2)^x + 50
• y = 50(1.4)^x

Multiple Choice

Is the pictured graph exponential growth, exponential decay, or linear or none?

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

What is the equation of the horizontal asymptote for following exponential function?

• y = -4

• y > -4

• y < -4

• (0, -3)

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​Domain
Range
intercept
asymptote

End Behavior

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Multiple Choice

What is the domain and range of the function y=2^x ?
Use the graph to help!

•  Domain: −∞<x<∞
  Range: y>0
• Domain: −∞<x<∞
  Range: y>1
• Domain: −2<x<∞
  Range: y>0
• Domain: −∞<x<∞
  Range: y>0

Multiple Choice

Given y=3^x determine the y-intercept 

• (0,1)
• (0,3)
• No Y-intercept
• y=1

Learning Outcomes

​By the end of the lesson student will be able to

Graph transformation of exponential functions.
Analyze graphs of exponential functions
Interpret Exponential functions
Compare exponential functions

​Types of Transformations

​Analyzing Transformations

f(x) = 2^x

(Parent Function)

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

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

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​Exponential Growth Function

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