Rational Functions and End Behavior
Alice White
7 min read
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Study Guide Overview
This study guide covers rational functions and their end behavior. It explains how to identify rational functions, analyze their end behavior based on the degrees of the numerator and denominator polynomials, and determine horizontal and slant asymptotes. It also covers expressing end behavior using limits, and provides practice questions and exam tips.
#AP Pre-Calculus: Rational Functions & End Behavior 🚀
Hey there, future AP Pre-Calc master! Let's dive into the world of rational functions and their end behavior. This guide is designed to be your go-to resource the night before the exam. Let's make sure you're feeling confident and ready to ace it! 💪
#1.7: Rational Functions and End Behavior
#What are Rational Functions? 🤔
Remember our polynomial friends? Well, rational functions are like their cool cousins! A rational function is simply a ratio (or quotient) of two polynomial functions. Think of it like this:
The degree of the polynomials in the numerator and denominator dictates the function's behavior. It's all about how these polynomials compare to each other as x gets really big (or really small).
Think of rational functions as a fraction of polynomials. The numerator and denominator are both polynomials. The relationship between their degrees determines the end behavior.
Image: A visual of a rational expression, showing a polynomial divided by another polynomial.
#End Behavior: What Happens at the Edges? 🧐
End behavior describes what happens to the function as x approaches positive or negative infinity. We're looking at the degrees of the polynomials in the numerator and denominator to figure this out. The polynomial with the higher degree will have the greatest influence on the overall behavior of the rational function.
Focus on the leading terms of the numerator and denominator polynomials. Th...
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