n this section we’re going to review one of the more common functions in both
calculus and the sciences. However, before getting to this function let’s take a much
more general approach to things.
Let’s start with
,
. An exponential function is then a
function in the form,
Note that we avoid
because that would give the constant
function,
. We avoid
since this would also
give a constant function and we avoid negative values of
b
for the following reason.
Let’s, for a second, suppose that we did allow
b
to be negative and look at the
following function.
Let’s do some evaluation.
So, for some values of
x
we will get real numbers and for other values of
x
we well get
complex numbers. We want to avoid this and so if we require
this
will not be a problem.
Let’s take a look at a couple of exponential functions.
Example 1
Sketch the graph of
and
Solution
Let’s first get a table of values for these two functions.
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 Fall '08
 sc
 Calculus, Exponential Function, Derivative, Complex number

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