Describe End Behavior

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.

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

Determine the end behavior: 2. 3x7 + 8x2 + 4x – 13 = 0 Leading Coefficient → POSITIVE → right side up Degree → ODD → arms opposite

Determine the end behavior: 3. -2x5 + x4 - 6x2 – 8x = 0 Leading Coefficient → NEGATIVE → right arm down Degree → ODD → arms apart

Determine the end behavior: 4. -2x2 – 6x + 6 = 0 Leading Coefficient → NEGATIVE → right arm down Degree → EVEN → arms together

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

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

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

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

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

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