1. 7.2 PROPERTIES OF
EXPONENTIAL
FUNCTIONS

2. Transformations of Exponential
Functions
Note that the base of the parent is a variable,
 Parent: therefore there are infinite “parents” within the
Exponential Family
 General Form:
 Stretch:
 Compression (shrink):
 Reflection:
 Horizontal Translation:
 Vertical Translation:

3. Graph each function as a
transformation of its parent
1. Create a Table of Values for the parent
2. Plot the points and label the graph
3. If the transformation contains a
stretch, compression, or reflection: Create a
Table of Values for the transformed function
(use the same x-values) and Plot the points
and label the graph
4. If the transformation contains a simple
horizontal or vertical translation: move the
parent points appropriately

4. Examples

5. Examples

6. Examples

7. The Number e
 The Number e is an irrational number
approximately equal to 2.71828
 Exponential functions with base e are called
natural base exponential functions.
 These exponential functions have the same
properties as other exponential functions
 To graph functions with base e, use the “e” key on
the calculator to get a decimal approximation

8. Continuously Compounded
Interest
To use this function:
1. Identify the value of the variables
2. Plug the known values into the equation
3. Solve for the unknown value

9. Example (p447)
Suppose you won a contest at the start of 5th
grade that deposited $3000 in an account that
pays 5% annual interest compounded
continuously. How much will you have in the
account when you enter high school 4 years
later? Express the answer to the nearest
dollar.

10. Homework
 P447 #1 – 4 all, 7 – 27 odd, 28 – 31 all