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PreAP Algebra 2 Unit 8 Lesson 3 End behavior of rational functions Objectives: Students will be able to: Determine end behavior by dividing and seeing what terms drop out as x Know that there will
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01
To fill out finding end behavior of a function, follow these steps:
02
Start by examining the degree of the polynomial function.
03
If the degree is odd (i.e., a positive integer), then the end behavior will be opposite for positive and negative values of x. This means that as x approaches positive infinity, the function will either go to positive infinity or negative infinity, depending on the leading coefficient. Similarly, as x approaches negative infinity, the function will go to the corresponding opposite infinity.
04
If the degree is even (i.e., a positive integer), then the end behavior will be the same for positive and negative values of x. This means that as x approaches positive infinity, the function will either go to positive infinity or negative infinity, depending on the leading coefficient. Similarly, as x approaches negative infinity, the function will also go to the same infinity as it approaches positive infinity.
05
Take note of any horizontal asymptotes, if present, as they can provide additional information about the end behavior.
06
Use these observations to graph the function and determine its end behavior accurately.

Who needs finding end behavior of?

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Finding end behavior of a function is important for mathematicians, students studying calculus or algebra, and anyone dealing with polynomial functions. It helps in understanding the long-term behavior of the function and can provide insights into its graph and properties.
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Finding end behavior refers to determining the long-term trends of a function as it approaches positive and negative infinity.
Typically, individuals or entities that are engaged in specific financial, academic, or statistical analyses are required to file findings related to end behavior.
Filling out a finding end behavior report generally involves analyzing the function, providing specific evaluations at extreme values, and documenting findings according to preset guidelines.
The purpose of finding end behavior is to understand the overall trend or behavior of a function at its extremes, which aids in graphing and analyzing the function.
Information that must be reported typically includes the limits of the function as x approaches both positive and negative infinity, and any relevant asymptotic behavior.
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