Section 14.2 Graphs and End Behavior of Exponential Functions
Fact 14.12. Finding the Graph of an Exponential Function.
For our usual exponential functions


Fact 14.14. Finding End Behavior of an Exponential Function.
To find the end behavior of an exponential function, we first need to figure out whether it represents growth or decay. After that, we can use the shape of the graph to determine the end behavior.

For functions with exponential growth, we have the following end behavior.
The end behavior on the left (as
), it has a horizontal asymptote at *The end behavior on the right (as
),

For functions with exponential decay, we have the following end behavior.
The end behavior on the left (as
),The end behavior on the right (as
), it has a horizontal asymptote at *.
*Warning: Vertical shifts in the formula could change the value of the horizontal asympote
Example 14.15.
Suppose we want to find the end behavior of
As
As
Checkpoint 14.16.
Find the end behavior of the function
Example 14.17.
Suppose we want to find the end behavior of
As
As
Checkpoint 14.18.
Find the end behavior of the function
As
As
Since
As
As