Section 4.3
The Graphs of Polynomial Functions
Objective 1:
Understanding the Definition of a Polynomial Function
Definition
Polynomial Function
The function
1
2
1
0
1
2
( )
n
n
n
n
n
n
f x
a x
a
x
a
x
a x
a




=
+
+
+
+
+
L
is a polynomial function
of degree
n
where
n
is a nonnegative integer.
The numbers
0
1
2
,
,
,
,
n
a
a
a
a
K
are called
the
coefficients
of the polynomial function. The number
n
a
is called
the leading
coefficient
and
0
a
is called the
constant coefficient
.
4.3.1, 2, and 4
Determine if the given function is a polynomial function.
If it is, then identify the degree, the leading
coefficient, and the constant coefficient.
(Type N is the function is not a polynomial function.)
a)
f(x) =
_________________________
b)
f(x) =
_________________________
Degree _______
Degree _______
Leading Coefficient
_______
Leading Coefficient
_______
Constant Coefficient
_______
Constant Coefficient
_______
Objective 2:
Sketching the Graphs of Power Functions
(a)
( )
f x
x
=
(b)
2
( )
f x
x
=
(c)
3
( )
f x
x
=
(d)
4
( )
f x
x
=
(e)
5
( )
f x
x
=
4.3.10 and 15
Use the associated power function and transformations to sketch the following functions.
a)
f(x) =
___________________________
b)
f(x) =
___________________________
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Odd degree polynomials
have opposite lefthand and
righthand end behavior.
Even degree polynomials
have the same lefthand and
righthand end behavior.
Objective 3:
Determining the End Behavior of Polynomial Functions
Process for Determining the End Behavior of a Polynomial Function
1
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 Spring '09
 moshe
 Algebra, polynomial function

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