How to Find the Degree and Sign of a Polynomial Function
+xeven
–xeven
+xodd
–xodd
As x → ∞
f(x) → ∞
As x → –∞
f(x) → ∞
As x → ∞
f(x) → –∞
As x → –∞
f(x) → –∞
As x → ∞
f(x) → ∞
As x → –∞
f(x) → –∞
As x → ∞
f(x) → –∞
As x → –∞
f(x) → ∞
Right arrow UP = POSITIVE
Arrows opposite directions degree is
ODD number.
4 bumps therefore degree is 5 or higher:
5,7,9,11,13, etc.
Right arrow UP = POSITIVE
Arrows same direction degree is
EVEN number.
5 bumps therefore degree is 6 or
higher: 6,8,10,12,14, etc.
Right arrow UP = POSITIVE
Arrows opposite directions degree is
ODD number.
4 bumps therefore degree is 5 or higher:
5,7,9,11,13, etc.
Right arrow DOWN = NEGATIVE
Arrows opposite direction degree is
ODD number.
2 bumps therefore degree is 3 or
higher: 3,5,7,9, etc.
Right arrow UP = POSITIVE
Arrows same direction degree is
EVEN number.
7 bumps therefore degree is 8 or
higher: 8,10,12,14, etc.
Right arrow DOWN = NEGATIVE
Arrows same direction degree is
EVEN number.
3 bumps therefore degree is 4 or
higher: 4,6,8,10,12,14, etc.
Right arrow UP = POSITIVE
Arrows opposite directions degree is
ODD number.
2 bumps therefore degree is 3 or higher:
3,5,7,9,11,13, etc.
Right arrow DOWN = NEGATIVE
Arrows opposite direction degree is
ODD number.
6 bumps therefore degree is 7 or
higher: 7,9,11,13, etc.
Right arrow UP = POSITIVE
Arrows opposite directions degree is
ODD number.
4 bumps therefore degree is 5 or higher:
5,7,9,11,13, etc.
Right arrow UP = POSITIVE
Arrows same direction degree is EVEN
number.
3 bumps therefore degree is 4 or higher:
4,6,8,10,12,14, etc.
Right arrow DOWN = NEGATIVE
Arrows opposite direction degree is
ODD number.
4 bumps therefore degree is 5 or
higher: 5,7,9, 11,13etc.
Right arrow DOWN = NEGATIVE
Arrows opposite direction degree is
ODD number.
6 bumps therefore degree is 3 or
higher: 7,9, 11,13etc.
Note: A polynomial function
will AT MOST have one fewer
bumps than the degree of the
power function.
The DEGREE of the function is
determined by the direction of
the arrows.
1. If the arrows BOTH go
UP OR DOWN, the
function has an EVEN
degree
2. If the arrows go in
OPPOSITE directions,
the function has an ODD
degree.
3. If the rightmost arrow
goes UP, the function is
POSITIVE.
4. If the rightmost arrow
goes DOWN, the
function is
NEGATIVE.
5. Count the number of
BUMPS on the function
and ADD ONE. That is
the minimum
DEGREE of the function.