Describe End Behavior End behavior of a graph
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. 4 x 4 – 2 x 3 + 6 x – 3 = 0 Leading Coefficient → POSITIVE → right side up Degree → EVEN → arms together
Determine the end behavior: 2. 3 x 7 + 8 x 2 + 4 x – 13 = 0 Leading Coefficient → POSITIVE → right side up Degree → ODD → arms opposite
Determine the end behavior: 3. -2 x 5 + x 4 - 6 x 2 – 8 x = 0 Leading Coefficient → NEGATIVE → right arm down Degree → ODD → arms apart
Determine the end behavior: 4. -2 x 2 – 6 x + 6 = 0 Leading Coefficient → NEGATIVE → right arm down Degree → EVEN → arms together
Identify the leading coefficient, degree, and end behavior. 5. Q(x) = –x 4 + 6 x 3 – x + 9 negative -1 The leading coefficient is ____, which ______. even 4 The degree is ____, which ______. 6. P(x) = 2 x 5 + 6 x 4 – x + 4 positive 2 The leading coefficient is _____, which ______. odd 5 The degree is _____, which ______.
Identify the leading coefficient, degree, and end behavior. 7. P(x) = -2 x 5 + x 4 - 6 x 2 – 8 x negative -2 The leading coefficient is ____, which ______. odd 5 The degree is ____, which ______. 8. S(x) = – 2 x 2 -6 x + 6 negative -2 The leading coefficient is ____, which ______. even 2 The degree is ____, which ______.
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. negative LC_____ 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. positive LC_____ even degree_____
Example 11 Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. negative LC_____ odd degree_____
Example 12 Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient. positive LC_____ even degree_____
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