How to Find the End Behavior of Polynomials?
The end behavior of a polynomial function is the behavior of the graph \(f (x)\) where \(x\) approaches infinitely positive or infinitely negative. Here you will learn how to find the end behavior of a polynomial.
![How to Find the End Behavior of Polynomials?](https://www.effortlessmath.com/wp-content/uploads/2022/03/Blog-End-Behavior-of-Polynomials-512x240.jpg)
To predict the end behavior of a polynomial function, first, check whether the function is an odd-degree or even-degree function and whether the leading coefficient is positive or negative.
Related Topics
A step-by-step guide to end behavior of polynomials
The end behavior of a polynomial function describes how the graph behaves as \(x\) approaches \(±∞\). We can determine the end behavior by looking at the leading term (the term with the highest \(n\)-value for \(ax^n\), where \(n\) is a positive integer and \(a\) is any nonzero number) of the function.
The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. Therefore, the leading coefficient sign is sufficient to predict the end behavior of the function.
Depending on the sign of the coefficient \((a)\) and the parity of the exponent \((n)\), the end behavior differs:
![](https://www.effortlessmath.com/wp-content/uploads/2022/03/Untitled22.png)
End Behavior of Polynomials – Example 1:
Find the end behavior of the function \(f(x)= x^4-4x^3+3x+25\).
Solution:
The degree of the function is even and the leading coefficient is positive. So, the end behavior is:
\(f(x)\)→\(+∞\), as \(x\) →\(−∞\)
\(f(x)\)→\(+∞\), as \(x\) →\(+∞\)
Exercises for End Behavior of Polynomials
Find the end behavior of each function.
- \(\color{blue}{f(x)=-x^5+4x^3-9x , x→−∞}\)
- \(\color{blue}{f(x)=6x^6-4x^4+2x-3, x→+∞}\)
- \(\color{blue}{f(x)=(x+4)^2+x^4+3, x→-∞}\)
- \(\color{blue}{f(x)=-8x^4+3x^3+11x^2+7, x→+∞}\)
![This image has an empty alt attribute; its file name is answers.png](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
- \(\color{blue}{f(x)→+∞}\)
- \(\color{blue}{f(x)→+∞}\)
- \(\color{blue}{f(x)→+∞}\)
- \(\color{blue}{f(x)→-∞}\)
Related to This Article
More math articles
- Number Properties Puzzle – Challenge 16
- 5 Best Mini Laptops to Use Anytime, Anywhere
- An In-depth Exploration of How to Find the Codomain
- Full-Length 7th Grade PSSA Math Practice Test-Answers and Explanations
- How to Interpret STAAR Scores?
- Types Of Angles In Geometry
- 6th Grade OST Math Practice Test Questions
- The Ultimate 7th Grade MAAP Math Course (+FREE Worksheets)
- Why Do Most Students Struggle with Math?
- The Ultimate 7th Grade OST Math Course (+FREE Worksheets)
What people say about "How to Find the End Behavior of Polynomials? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.