Section 5.1a Exponential Functions
Objective 1: Understanding the Characteristics of Exponential Functions
Definition of an Exponential Function
An exponential function is a function of the form
( ) x
f x b
where x is any real number and
0b
such that
1b
. The constant, b, is called the base of the exponential function.
Characteristics of Exponential Functions
For
0b
,
1b
the exponential function with base b is defined by
( ) x
f x b
.
The domain of
( ) x
f x b
is
,
and the range is
0,
. The graph of
( ) x
f x b
has one of the
following two shapes
( ) x
f x b
,
1b
( ) x
f x b
,
0 1b
The graph intersects the y-axis at
0 1,
. The graph intersects the y-axis at
0 1,
.
The line
0y
is a horizontal asymptote. The line
0y
is a horizontal asymptote.
5.1.3
Sketch the graph of the exponential function
f(x) = ______.
5.1.6
Determine the correct exponential function
of the form
( ) x
f x b
whose graph is given.
f(x) = __________________________
