# 1.6 Polynomial Functions and End Behavior

The end behavior of polynomial functions is determined by their degree.
Polynomial Functions and End Behavior

# Polynomial Functions and End Behavior

The end behavior of polynomial functions is determined by their degree (highest power of x) and the sign of their leading coefficient (the coefficient of the term with the highest power). This behavior describes how the function behaves as x approaches positive or negative infinity.

## Examples

Below are ten examples illustrating different end behaviors based on the degree and leading coefficient:

1. Function: f(x) = x^3. As x -> ∞, f(x) -> ∞; as x -> -∞, f(x) -> -∞.
2. Function: f(x) = -2x^4. As x -> ∞ or x -> -∞, f(x) -> -∞.
3. Function: f(x) = 3x^2 - x. As x -> ∞ or x -> -∞, f(x) -> ∞.
4. Function: f(x) = x^5 - 4x^3 + 2x. As x -> ∞, f(x) -> ∞; as x -> -∞, f(x) -> -∞.
5. Function: f(x) = -x^6 + 5x^4 - 3x^2 + 2. As x -> ∞ or x -> -∞, f(x) -> -∞.
6. Function: f(x) = 4x^3 + 3x^2 - 2x + 1. As x -> ∞, f(x) -> ∞; as x -> -∞, f(x) -> -∞.
7. Function: f(x) = -0.5x^5 + 100. As x -> ∞, f(x) -> -∞; as x -> -∞, f(x) -> ∞.
8. Function: f(x) = 2x^7 - 7x^5 + 4. As x -> ∞, f(x) -> ∞; as x -> -∞, f(x) -> -∞.
9. Function: f(x) = -3x^2 + 6x - 9. As x -> ∞ or x -> -∞, f(x) -> -∞.
10. Function: f(x) = x^8 + 4x^4 - 2. As x - 
 
 
 
 
 
 /*! elementor - v3.23.0 - 05-08-2024 */ .elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block} Packetappc_1.6_packet.pdfDownload FilePractice Solutionsappc_1.6_solutions.pdfDownload FileCorrective Assignmentsappc_1.6_ca1.pdfDownload Fileappc_1.6_ca2.pdfDownload FileAP Learning Objectives: ​1.6.A  Describe end behaviors of polynomial functions. 
 
 Tags:AP Precalculus 
 Shares:
 
 Previous Post1.5B Even and Odd PolynomialsNext PostUnit 1A Review Related Posts GCSE KS3 Maths Study Notes, Practice Papers, Exam Tips 1znmx3 months ago AP Precalculus 1.4 Polynomial Functions and Rates of Change 1znmx5 months ago AP Precalculus Unit 1A Review 1znmx5 months ago AP Precalculus 1.5B Even and Odd Polynomials 1znmx5 months ago GCSE Mathematics Notes & Practice Sheets for GCSE/IGCSE Edexcel 1znmx3 months ago Leave a Reply Your email address will not be published. Required fields are marked * Save my name, email, and website in this browser for the next time I comment. Δdocument.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); {"@context":"https:\/\/schema.org","@type":"Article","dateCreated":"2024-03-23T21:00:46+00:00","datePublished":"2024-03-23T21:00:46+00:00","dateModified":"2024-03-23T21:01:57+00:00","headline":"1.6 Polynomial Functions and End Behavior","name":"1.6 Polynomial Functions and End Behavior","keywords":"AP Precalculus","url":"https:\/\/revisiontown.com\/1-6-polynomial-functions-and-end-behavior\/","description":"The end behavior of polynomial functions is determined by their degree.","copyrightYear":"2024","publisher":{"@id":"#Publisher","@type":"Organization","name":"RivisionTown","logo":{"@type":"ImageObject","url":"https:\/\/revisiontown.com\/wp-content\/uploads\/2023\/10\/revisiontown.png"}},"sourceOrganization":{"@id":"#Publisher"},"copyrightHolder":{"@id":"#Publisher"},"mainEntityOfPage":{"@type":"WebPage","@id":"https:\/\/revisiontown.com\/1-6-polynomial-functions-and-end-behavior\/"},"author":{"@type":"Person","name":"1znmx","url":"https:\/\/revisiontown.com\/author\/1znmx\/"},"articleSection":"AP Precalculus,Unit 1A - Polynomial and Rational Functions","image":{"@type":"ImageObject","url":"https:\/\/revisiontown.com\/wp-content\/uploads\/2024\/03\/1.6-Polynomial-Functions-and-End-Behavior-.png","width":800,"height":600}}