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Section 2.2 – Polynomial Functions
1
Section 2.2
Polynomial Functions
Definition of a Polynomial Function
Let
n
be a nonnegative integer and let
0
1
2
1
,
,
,...,
,
a
a
a
a
a
n
n

, be real numbers, with
0
≠
n
a
.
The function defined by
0
1
2
2
...
)
(
a
x
a
x
a
x
a
x
f
n
n
+
+
+
+
=
is called a
polynomial
function of
x
of degree
n
.
The number
n
a
, the coefficient of the variable to the highest
power, is called the
leading coefficient
.
For example,
234
.
0
10
3
1
6
3
2
)
(
x
x
x
x
p


=
is NOT a polynomial, but
x
x
x
x
a
234
.
0
3
1
2
)
(
10
3
+

=
is a polynomial.
The domain of any polynomial function is all real numbers.
End Behavior of Polynomial Functions
The behavior of a graph of a function to the far left or far right is called its
end behavior.
Evendegree
LEADING COEFFIECIENT:
+
LEADING COEFFICIENT:

Odddegree
LEADING COEFFIECIENT:
+
LEADING COEFFICIENT:

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View Full Document Section 2.2 – Polynomial Functions
2
Power Functions
A
power function
is a polynomial that takes the form
n
ax
x
f
=
)
(
, where
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This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.
 Fall '08
 Staff
 Real Numbers

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