1. Lesson 3.6b Graphing & Identifying Key Features of Exponential Functions
Concept: Characteristics of Exponential Functions
Lesson EQ: How do you graph, interpret, and apply the key features of an exponential function? (Standard F.IF.4,5,7)
Vocabulary:
Domain, Range, & End Behavior

2. Exponential Functions
Recall
General form 𝒇 𝒙 =𝒂 𝒃 𝒙 +𝒌 a = initial value that determines the shape a > 1 stretch; 0 < a < 1 shrink; -a = reflection b = growth if the value is > 1 b = decay if the value is between 0 and 1 k = horizontal asymptote & vertical shift

3. Guided Practice: Example 1, continued
Complete the table of values to create a graph of the function.
𝑓 𝑥 = 2 𝑥 x
f(x) –2 –1 1 2
3.4.2: Graphing Exponential Functions

4. Domain
The collection of all x-values (inputs). For exponential functions the domain will always be all real numbers ℝ. Example: 𝒇 𝒙 = 𝟐 𝒙 Domain = all real numbers because any number can be used as x.

5. Range
The collection of all y-values (outputs). +a: Range is all numbers > asymptote. -a: Range is all numbers < asymptote. Example: 𝒇 𝒙 = 𝟐 𝒙 Domain = all numbers > asymptote. y > 0

6. What happens at the ends of the graph.
End Behavior
What happens at the ends of the graph.
Exponential functions have 2 end behaviors. One towards + or - infinity and one towards the horizontal asymptote.
Example: 𝒇 𝒙 = 𝟐 𝒙
Left: As x → -∞, y → 0
Right: As x → +∞, y → +∞

7. Guided Practice: Example 2, continued
Complete the table of values to create a graph of the function.
𝑓 𝑥 = 𝑥 x
f(x) –2 –1 1 2
3.4.2: Graphing Exponential Functions

8. Example 2: 𝑓(𝑥) = 1 2 𝑥 Recall Not a reflection Decay
Horizontal Asymptote:
y = 0
y-intercept: (0, 1)
Domain = _____________
Range = all numbers ____ asymptote
y ____ _____
End behavior:
Left: As x → -∞, y → ___
Right: As x → +∞, y → ___

9. Guided Practice: Example 3, continued
Complete the table of values to create a graph of the function.
𝑓 𝑥 = 3 𝑥 +1 x
f(x) –2 –1 1 2
3.4.2: Graphing Exponential Functions

10. Example 3: 𝑓 𝑥 = 3 𝑥 +1 Recall Not a reflection Growth
Horizontal Asymptote:
y = 1
y-intercept: (0, 2)
Domain = _____________
Range = all numbers ____ asymptote
y ____ _____
End behavior:
Left: As x → -∞, y → ___
Right: As x → +∞, y → ___

11. Guided Practice: Example 4, continued
Complete the table of values to create a graph of the function.
𝑓 𝑥 =−1( 2) 𝑥 +3 x
f(x) –2 –1 1 2
3.4.2: Graphing Exponential Functions

12. Example 4: 𝑓 𝑥 =−1( 2) 𝑥 +3 Recall Reflection Decay
Horizontal Asymptote:
y = 3
y-intercept: (0, 2)
Domain = _____________
Range = all numbers ____ asymptote
y ____ _____
End behavior:
Left: As x → -∞, y → ___
Right: As x → +∞, y → ___

13. Summarizing Strategy: Example for Absent friend
Your absent friend needs you to show them an example of what they missed.
Choose 3 of the following 5 features to identify for this exponential function: f(x) = 3x – 2
Asymptote
y-intercept
Domain
Range
End Behavior