How to find the end behavior of a polynomial function?
Understand the Problem
The question is asking for the methods or steps to determine the end behavior of a polynomial function, which involves analyzing how the function behaves as the input values approach positive or negative infinity.
Answer
Analyze the leading term's degree and coefficient.
Find the leading term of the polynomial function and use its degree and coefficient to determine how the graph behaves as x approaches positive and negative infinity.
Answer for screen readers
Find the leading term of the polynomial function and use its degree and coefficient to determine how the graph behaves as x approaches positive and negative infinity.
More Information
Examining the leading term for end behavior helps simplify the analysis because this term grows the fastest as x becomes very large or very small.
Tips
A common mistake is to consider all terms of the polynomial instead of focusing solely on the leading term.
Sources
- Power Functions and Polynomial Functions - math.libretexts.org
- End Behavior of a Function - Varsity Tutors - varsitytutors.com
- Intro to end behavior of polynomials (video) - Khan Academy - khanacademy.org
