Exponential Function - Definition

1
Exponential Function - Definition

• The exponential function is given by ...

where x is any real number and ...

• Example 1

f is an exponential function where the base is 3
and the exponent is x.

• Example 2

g is not an exponential function since b -3 lt 0.
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Exponential Function - Definition

• Why is it necessary to have the restrictions on
  the base b? Consider the following examples.

• Example 3

For all values of x, f(x) 1. This reduces the
equation to the simple linear equation, y 1,
which is not exponential.

• Example 4

Using the table feature on a graphing calculator
yields ...
Slide 2
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Exponential Function - Definition

• Note that the data represents points on a graph
  that keep jumping from positive to negative to
  positive y-values. The points on the
  graph are not connected like most graphs are.

• Another problem is what to do when x 1/2,
  where

which is complex.
Slide 3
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Exponential Function - Definition

• Remember that the exponential function is quite
  different from a polynomial function.

Polynomial Function
Exponential Function
?
?
?
?

• The polynomial function has a variable base ...

• The exponential function has a constant base ...

and a constant exponent.
and a variable exponent.
Slide 4
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Exponential Function - Definition
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