8.1 Graphing Exponential Functions
Exponential Functions:
· the base is a constant
· the exponent is a variable
Some examples of exponential functions:
1
Exponential functions are equations of form:
with base b where
,
, and
Characteristics of Exponential Functions:
- Continuous and one-to-one
- Domain is
- Range is
if a > 0
- Range is
if a < 0
- (0, a) is the y-intercept
Not the case if a term is added/subtracted
to exponential term:
For example,
We will do an example like this later in the
lesson.
2
Exponential Growth vs. Exponential Decay
If a is positive,
can be classified as
exponential growth or exponential decay.
In the case where a is positive:
If
, then the function is classified as
exponential growth.
If
, then the function is classified as
exponential decay.
If a is negative, then it's neither exponential growth
nor exponential decay.
Examples:
Exp. Growth
Exp. Decay
Neither
3
Vocab: an asymptote is a line that a graph approaches
(but rarely crosses) as
or as
Graphs of Exponential Functions
Example 1) Graph the given function. State the domain
and range. List any asymptotes. Determine whether the
function is exp. growth, exp. decay, or neither.
a.
4
b.
5
c.
6
d.
7
For Exponential Functions of form:
is the horizontal asymptote
the vertical shift is
the horizontal shift is
units
units
8
Example 2) Graph the given function. State the domain
and range. List any asymptotes. Determine whether the
function is exp. growth, exp. decay, or neither. List any
translations.
a.
9
b.
10
Writing Exponential Functions
Example 3) Write an exponential function whose graph
passes through the given points.
a.
and
b.
and
11