3.2: Polynomial Functions of Higher Degree
So far, we have only graphed two kinds of polynomial functions this semester:
lines and parabolas.
In this section we will graph polynomials of degree 3 or higher.
All polynomial functions have graphs that are
smooth continuous curves
. In this class, when we say a
graph is smooth, we mean that it has no sharp corners. And a graph that is continuous has no holes or
breaks. For example, the following graphs are
not
polynomial functions.
(Continuous, but not smooth)
(Not continuous)
x
y
x
y
The General Form of a Polynomial
a
n
x
n
+
a
n
1
x
n
1
+ . . . +
a
1
x
+
a
0
.
˚
a
n
x
n
is the
leading
term
,
a
n
is the
leading
coefficient,
and the
degree
of the polynomial is
n
Example:
P
(
x
) =
x
3
+ 6
x
 8
the leading coefficient is 1,
the degree of the polynomial is 3
F
AR
L
EFT AND
F
AR
R
IGHT
B
EHAVIOR
n
is even
n
is odd
a
n
> 0
up
to the farleft
up
to the farright
down
to the farleft
up
to the farright
a
n
< 0
down
to the farleft
down
to the farright
up
to the farleft
down
to the farright
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 Spring '08
 MatRoy
 Polynomials, polynomial functions, higher degree, polynomial function, 2 °

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