End Behavior of Polynomials: Determining the Upward and Downward Trends, Study notes of Mathematics

Download End Behavior of Polynomials: Determining the Upward and Downward Trends and more Study notes Mathematics in PDF only on Docsity!

Notes: End Behavior

I. End Behavior of Functions

The end behavior of a graph describes the far left and the far right portions of the graph.

Using the leading coefficient and the degree of the polynomial, we can determine the end behaviors of the graph. This is often called the Leading Coefficient Test.

END BEHAVIOR

Degree: Even

End Behavior: Down Down

f ( x )   x

Leading Coefficient:

END BEHAVIOR

Degree: Odd

Leading Coefficient: +

End Behavior: Down Up

f ( x )  x

Examples: Describe the end behavior of the following function:

First determine whether the degree of the polynomial is even or odd.

Next determine whether the leading coefficient is positive or negative.

degree = 2 so it is even

Leading coefficient = 2 so it is positive

f ( x )  2 x^2  3 x  5

PRACTICE: Describe the End Behavior:

a. ( ) 2 5 9

f x   x  x 

b. ( ) 4 2 6 3

f x  x  x  x 

degree = 3 so it is odd Leading coefficient = -2 so it is negative 𝑦 → ∞ 𝑎𝑠 𝑥 → −∞, 𝑦 → −∞ 𝑎𝑠 𝑥 → ∞

degree = 4 so it is even Leading coefficient = 4 so it is positive 𝑦 → ∞ 𝑎𝑠 𝑥 → −∞, 𝑦 → ∞ 𝑎𝑠 𝑥 → ∞