1. Characteristics of Exponential Functions

2. A function that can be expressed in the form
and is positive, is called an Exponential Function.
Exponential Functions with positive values of x are increasing, one-to-one functions.
The parent form of the graph has a y-intercept at (0,1) and passes through (1,b).
The value of b determines the steepness of the curve.
The function is neither even nor odd. There is no symmetry.
There is no local extrema.

3. More Characteristics of
The domain is
The range is
End Behavior: As
The y-intercept is
The horizontal asymptote is
There is no x-intercept.
There are no vertical asymptotes.
This is a continuous function.
It is concave up.

4. How would you graph How would you graph Domain: Range: Y-intercept:
Horizontal
Asymptote:
Inc/dec?
increasing
Concavity? up
How would you graph
Domain:
Range:
Y-intercept:
Horizontal
Asymptote:
Inc/dec?
increasing
Concavity? up

5. Recall that if then the graph of is a reflection of about the y-axis.
Thus, if then
Domain:
Range:
Y-intercept:
Horizontal
Asymptote:
Concavity? up

6. Notice that the reflection is decreasing, so the end behavior is:
How would you graph
Is this graph increasing
or decreasing?
Decreasing.
Notice that the reflection is decreasing, so the end behavior is:

7. Transformations
Exponential graphs, like other functions we have studied, can be dilated,
reflected and translated.
It is important to maintain the same base as you analyze the transformations.
x-axis
Vertical stretch 3
Vertical shift down 1
Vertical shift up 3

8. More Transformations Reflect about the x-axis. Vertical shrink ½ .
Horizontal shift left 2.
Horizontal shift right 1.
Vertical shift up 1.
Vertical shift down 3.
Domain:
Domain:
Range:
Range:
Horizontal
Asymptote:
Horizontal
Asymptote:
Y-intercept:
Y-intercept:
Inc/dec?
decreasing
Inc/dec?
increasing
Concavity?
down
Concavity? up