63: Exponential Functions
Exponential function is a function in the form
f(x) =
a
x
where
a
is a positive real number and
a
≠
1.
The domain of
f
is the set of all real numbers.
The laws of exponents for real (irrational)
exponents are the same as those for integer and rational exponents.
Irrational exponents are
truncated to a finite number of digits, so that
a
r
≈
a
x
.
The number
e
is the number that
1
1
+
F
H
G
I
K
J
n
n
approaches as n
→∞
.
f(x) = a
x
Range
xintercept
yintercept
Horizontal
asymptote
Charac
teristic
Passes
through
a > 1
(0,
∞
)
None
(0, 1)
xaxis as
x
→

∞
Increasing,
onetoone
(0, 1)
(1, a)
0 < a < 1
(0,
∞
)
None
(0, 1)
xaxis as
x
→∞
Decreasing
onetoone
(0, 1)
(1, a)
Approximate to three decimal places:
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 Fall '08
 Staff
 Exponential Function, Real Numbers, Exponents, Exponential Functions, Complex number, following exponential functions

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