Describe
End Behavior
End behavior of a graph describes the values of the function
as x approaches positive infinity and negative infinity
 x    goes to the right
negative infinity  x    goes to the left
positive infinity
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.
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
Determine the end behavior:
1. 4x4 – 2x3 + 6x – 3 = 0
Leading Coefficient → POSITIVE → right side up
Degree → EVEN → arms together
As x  , then P  x  
As x  , then P  x  


Determine the end behavior:
2.
3x7 + 8x2 + 4x – 13 = 0
Leading Coefficient → POSITIVE → right side up
Degree → ODD → arms opposite
As x  , then P  x  

As x  , then P  x  

Determine the end behavior:
3. -2x5 + x4 - 6x2 – 8x = 0
Leading Coefficient → NEGATIVE → right arm down
Degree → ODD → arms apart
As x  , then P  x  

As x  , then P  x   
Determine the end behavior:
4. -2x2 – 6x + 6 = 0
Leading Coefficient → NEGATIVE → right arm down
Degree → EVEN → arms together
As x  , then P  x  

As x  , then P  x  

Identify the leading coefficient, degree, and end behavior.
5. Q(x) = –x4 + 6x3 – x + 9
negative
-1
The leading coefficient is ____,
which ___________.
even
4
The degree is ________,
which ____________.

As x  , P  x   ______

As x  , P  x   ______
6. P(x) = 2x5 + 6x4 – x + 4
positive
2
The leading coefficient is _____,
which ____________.
odd
5
The degree is _________,
which ___________.
 As x  , P  x   ______
As x  , P  x   ______

Identify the leading coefficient, degree, and end behavior.
7. P(x) = -2x5 + x4 - 6x2 – 8x
negative
-2
The leading coefficient is ____,
which ___________.
odd
5
The degree is ________,
which ____________.

As x  , P  x   ______

As x  , P  x   ______
8. S(x) = –2x2 -6x + 6
negative
-2
The leading coefficient is ____,
which ___________.
even
2
The degree is ________,
which ____________.

As x  , P  x   ______
As x  , P  x   ______

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.

As x  , P  x   ______
negative
LC_____

As x  , P  x   ______
odd
degree_____
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.
As x  , P  x   ______

positive
LC_____

As x  , P  x   ______
even
degree_____
Example 11
Identify whether the function graphed has an odd or even degree
and a positive or negative leading coefficient.
 As x  , P  x   ______

As x  , P  x   ______
negative
LC_____
odd
degree_____
Example 12
Identify whether the function graphed has an odd or even degree
and a positive or negative leading coefficient.
As x  , P  x   ______

positive
LC_____

As x  , P  x   ______
even
degree_____