Class Graphing Activity
Graphing Polynomial Functions
Directions: Complete the chart below and use the information find the matching graph
from the following page.
Polynomial
Function
#1.
f (x) =
5
(x + 1)2 (x ! 1)(x ! 4)
6
#2.
f (x) = x 4 ! 2x 2 + 1
#3.
f (x) = !3x 5 + 2x 2 ! 7x + 1
#4.
f (x) = x 3 ! 5x
#5.
f (x) = !2x 4 + 4x 2 ! 2
#6.
f (x) = x 5 ! 2x 2 + 4
Degree
Leading
Coefficient
End
Behavior
Matching
Graph
Class Graphing Activity
Graphing Polynomial Functions
Graph a
6
Even or Odd Degree?
4
Positive or Negative
Leading Coefficient?
2
-10
-5
5
10
-2
End Behavior:
x ! "# , y !
x!#
, y!
-4
-6
Graph b
10
Even or Odd Degree?
5
-20
-10
10
-5
20
Positive or Negative
Leading Coefficient?
-10
-15
-20
-25
-30
End Behavior:
x ! "# , y !
x!#
, y!
Class Graphing Activity
Graphing Polynomial Functions
Graph c
10
Even or Odd Degree?
8
6
Positive or Negative Leading
Coefficient?
4
2
-10
-5
5
10
-2
End Behavior:
x ! "# , y !
x!#
, y!
-4
-6
-8
-10
Graph d
10
8
Even or Odd Degree?
6
4
Positive or Negative Leading
Coefficient?
2
-10
-5
5
-2
-4
-6
-8
-10
10
End Behavior:
x ! "# , y !
x!#
, y!
Class Graphing Activity
Graphing Polynomial Functions
Graph e
10
Even or Odd Degree?
8
6
Positive or Negative Leading
Coefficient?
4
2
-10
-5
5
10
-2
End Behavior:
x ! "# , y !
x!#
, y!
-4
-6
-8
-10
Graph f
10
8
Even or Odd Degree?
6
Positive or Negative Leading
Coefficient?
4
2
-10
-5
5
-2
-4
-6
-8
-10
10
End Behavior:
x ! "# , y !
x!#
, y!
Class Graphing Activity
Graphing Polynomial Functions
Directions: Complete the chart below and use the information find the matching graph
from the following page.
Polynomial
Function
Degree
Leading
Coefficient
4
5/6
x ! "#
x!#
,
,
y!#
y!#
b
#2.
f (x) = x 4 ! 2x 2 + 1
4
1
x ! "#
x!#
,
,
y!#
y!#
d
#3.
f (x) = !3x 5 + 2x 2 ! 7x + 1
5
-3
x ! "#
x!#
,
,
y!#
y ! "#
c
#4.
f (x) = x 3 ! 5x
3
1
x ! "#
x!#
,
,
y ! "#
y!#
e
#5.
f (x) = !2x 4 + 4x 2 ! 2
4
-2
x ! "#
x!#
,
,
y ! "#
y ! "#
a
#6.
f (x) = x 5 ! 2x 2 + 4
5
1
x ! "#
x!#
,
,
y ! "#
y!#
f
#1.
f (x) =
5
(x + 1)2 (x ! 1)(x ! 4)
6
End
Behavior
Matching
Graph
Class Graphing Activity
Graphing Polynomial Functions
Graph a
6
Even or Odd Degree?
4
Positive or Negative
Leading Coefficient?
2
-10
-5
5
10
-2
End Behavior:
x ! "# , y ! "#
x!#
, y ! "#
-4
-6
Graph b
10
Even or Odd Degree?
5
-20
-10
10
-5
20
Positive or Negative
Leading Coefficient?
-10
-15
-20
-25
-30
End Behavior:
x ! "# , y ! #
x!#
, y!#
Class Graphing Activity
Graphing Polynomial Functions
Graph c
10
Even or Odd Degree?
8
6
Positive or Negative Leading
Coefficient?
4
2
-10
-5
5
10
-2
End Behavior:
x ! "# , y ! #
x!#
, y ! "#
-4
-6
-8
-10
Graph d
10
8
Even or Odd Degree?
6
4
Positive or Negative Leading
Coefficient?
2
-10
-5
5
-2
-4
-6
-8
-10
10
End Behavior:
x ! "# , y ! #
x!#
, y!#
Class Graphing Activity
Graphing Polynomial Functions
Graph e
10
Even or Odd Degree?
8
6
Positive or Negative Leading
Coefficient?
4
2
-10
-5
5
10
-2
End Behavior:
x ! "# , y ! "#
x!#
, y!#
-4
-6
-8
-10
Graph f
10
8
Even or Odd Degree?
6
Positive or Negative Leading
Coefficient?
4
2
-10
-5
5
-2
-4
-6
-8
-10
10
End Behavior:
x ! "# , y ! "#
x!#
, y!#