#AP Pre-Calculus: Night Before Review 🚀

Hey! Let's get you prepped and confident for your AP Pre-Calculus exam. This guide is designed to be quick, clear, and super helpful for your last-minute review. Let's do this!

#1.11 Equivalent Representations of Polynomial and Rational Expressions

#Various Forms of Polynomial and Rational Expressions

Understanding how to switch between different forms of polynomial and rational expressions is KEY for the exam. Let's break it down:

#Factored Form

• What it is: A polynomial or rational function expressed as a product of its factors.

• #Why it's useful:

- Reveals **vertical asymptotes** and **holes** (removable discontinuities). - Provides insight into the **range** of the function.

![A function in its factored form.](https://user-images.githubusercontent.com/98941488/288914671-50612083-6e87-4124-8158-77279151899e.gif)

*Caption: A function in its factored form. Notice how the x-intercepts are easily visible.* 

#Standard Form

• What it is: A polynomial written in descending order of powers, or a rational function with polynomials in standard form in numerator and denominator.

• Why it's useful:

  • Determines end behavior of the function. 🧍
  • For polynomials:
    • Even degree with a positive leading coefficient: Ends go up (↑↑).
    • Even degree with a negative leading coefficient: Ends go down (↓↓).
    • Odd degree with a positive leading coefficient: Starts down, ends up (↗).
    • Odd degree with a negative leading coefficient: Starts up, ends down (↘).
  • For rational functions:
    • Numerator degree < denominator degree: Horizontal asymptote at y = 0. - Numerator degree = denominator degree: Horizontal asymptote at the ratio of leading coefficients.
    • Numerator degree > denominator degree: No horizontal asymptote (may have a slant asymptote).

  ![A function in its ...