1. Chapter 8-2 Properties of Exponential Functions
Essential Question: How do the “h” and “k” in y = ex – h + k affect the graph of y = ex?

2. 8-2: Properties of Exponential Functions
The function y = bx is called the parent function.
All exponential functions are called translations of the parent function.
Translations can be reflections, stretches/shrinks or shifts.

3. 8-2: Properties of Exponential Functions
The factor “a” in y = abx can represent a stretch, shrink and/or reflection
Stretches/Shrinks
If a is a number greater than 1, it stretches the parent function vertically
If a is a number less than 1, it shrinks the parent function vertically
y = 4(2)x
y = 2x
y = ¼(2)x

4. 8-2: Properties of Exponential Functions
The factor “a” in y = abx can represent a stretch, shrink and/or reflection
Reflection
If a is a negative number, its graph is a vertical reflection
y = 2x
y = -1(2)x

5. 8-2: Properties of Exponential Functions
Shifts
In the function y = abx-h + k:
Just like we did back with translations of an absolute value graph
h represents a horizontal shift (in the opposite direction)
k represents a vertical shift (in the correct direction)
y = (2)x+3
y = 2x
y = (2)x - 6

6. 8-2: Properties of Exponential Functions
Identify the parent function of y = 8(½)x+2+3, then identify any translations
Parent function: y = (½)x
Translations: Vertical stretch by a factor of Horizontal shift 2 units left Vertical shift 3 units up
Your turn: 9(3)x-3-1
Parent function:
Translations:
y=(3)x
Vertical stretch by a factor of 9
Horizontal shift 3 units right
Vertical shift 1 unit down

7. 8-2: Properties of Exponential Functions
The number e
Much like π, there is an irrational number e which gets used frequently when dealing with continuous growth. Your calculator has a key for ex
Evaluate e2 to four decimal places
Answer:
7.3891

8. 8-1: Exploring Exponential Models
Assignment
Page 442
Problems 1 – 14, 18 – 23 (all problems)
For problems 1 – 14:
Don’t graph the problems. Instead, identify the parent function and any translations that occur (like we did earlier today)