describe end behavior€¦ · it is helpful when you are graphing a polynomial function to know...
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Describe End Behavior
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 of a graph describes the values of the function as x approaches positive infinity and negative infinity
positive infinity x goes to the right
negative infinity x goes to the left
END BEHAVIOR – be the polynomial
Odd--then the left side and the right side are different
Even--then the left side and the right are the same
The Highest DEGREE is either even or odd
Negative--the right side of the graph will go down
The Leading COEFFICIENT is either positive or negative
Positive--the right side of the graph will go up
Determine the end behavior: 1. 4x4 – 2x3 + 6x – 3 = 0
Leading Coefficient →
Degree →
,As x then P x
,As x then P x
right side up POSITIVE →
EVEN → arms together
Determine the end behavior: 2. 3x7 + 8x2 + 4x – 13 = 0
Leading Coefficient →
Degree →
,As x then P x
,As x then P x
POSITIVE → right side up
arms opposite ODD →
Determine the end behavior: 3. -2x5 + x4 - 6x2 – 8x = 0
Leading Coefficient →
Degree →
,As x then P x
,As x then P x
right arm down NEGATIVE →
ODD → arms apart
Determine the end behavior: 4. -2x2 – 6x + 6 = 0
Leading Coefficient →
Degree →
,As x then P x
,As x then P x
NEGATIVE → right arm down
EVEN → arms together
Identify the leading coefficient, degree, and end behavior.
5. Q(x) = –x4 + 6x3 – x + 9
The leading coefficient is ____, which ___________.
The degree is ________, which ____________.
6. P(x) = 2x5 + 6x4 – x + 4
The leading coefficient is _____, which ____________.
The degree is _________, which ___________.
, ______As x P x , ______As x P x
, ______As x P x , ______As x P x
-1 negative
4 even
2 positive
5 odd
Identify the leading coefficient, degree, and end behavior.
7. P(x) = -2x5 + x4 - 6x2 – 8x
8. S(x) = –2x2 -6x + 6
The leading coefficient is ____, which ___________. -2 negative
The degree is ________, which ____________. 5 odd
, ______As x P x , ______As x P x
The leading coefficient is ____, which ___________. -2 negative
The degree is ________, which ____________. 2 even
, ______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 , ______As x P x
LC_____ degree_____ odd negative
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 , ______As x P x
LC_____ degree_____ positive even
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
LC_____ degree_____ negative odd
Example 12
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
LC_____ degree_____ positive even