1. Describe End Behavior

2. End behavior of a graph describes the values of the function as x approaches positive infinity and negative infinity
positive infinity
goes to the right
negative infinity
goes to the left
We look at the polynomials degree and leading coefficient to determine its end behavior.
It is helpful when you are graphing a polynomial function to know about the end behavior of the function.

3. END BEHAVIOR – be the polynomial
The Leading COEFFICIENT is either positive or negative
Positive--the right side of the graph will go up
Negative--the right side of the graph will go down
The Highest DEGREE is either even or odd
Even--then the left side and the right are the same
Odd--then the left side and the right side are different

5. Determine the end behavior:
1. 4x4 – 2x3 + 6x – 3 = 0
Leading Coefficient →
POSITIVE →
right side up
Degree →
EVEN →
arms together

6. Determine the end behavior:
x7 + 8x2 + 4x – 13 = 0
Leading Coefficient →
POSITIVE →
right side up
Degree →
ODD →
arms opposite

7. Determine the end behavior:
x5 + x4 - 6x2 – 8x = 0
Leading Coefficient →
NEGATIVE →
right arm down
Degree →
ODD →
arms apart

8. Determine the end behavior:
x2 – 6x + 6 = 0
Leading Coefficient →
NEGATIVE →
right arm down
Degree →
EVEN →
arms together

9. The leading coefficient is ____, which ___________. -1
Identify the leading coefficient, degree, and end behavior.
5. Q(x) = –x4 + 6x3 – x + 9
negative
The leading coefficient is ____, which ___________. -1 4
even
The degree is ________, which ____________.
6. P(x) = 2x5 + 6x4 – x + 4 2
positive
The leading coefficient is _____, which ____________.
odd
The degree is _________, which ___________. 5

10. The leading coefficient is ____, which ___________. -2
Identify the leading coefficient, degree, and end behavior.
7. P(x) = -2x5 + x4 - 6x2 – 8x
negative
The leading coefficient is ____, which ___________. -2
The degree is ________, which ____________. 5
odd
8. S(x) = –2x2 -6x + 6 -2
negative
The leading coefficient is ____, which ___________.
The degree is ________, which ____________. 2
even

11. Example 9 Using Graphs to Analyze Polynomial Functions
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
LC_____
negative
degree_____
odd

12. Example 10 Using Graphs to Analyze Polynomial Functions
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
LC_____
positive
degree_____
even

13. degree_____ LC_____ Example 11
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
LC_____
negative
degree_____
odd

14. LC_____ degree_____ Example 12
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
LC_____
positive
degree_____
even