#AP Pre-Calculus: Unit 1 Study Guide - Polynomial and Rational Functions

Welcome to your ultimate review for AP Pre-Calculus Unit 1! This guide is designed to help you feel confident and fully prepared for your exam. Let's dive in! 🚀

#🧐 What's the Point of AP Pre-Calculus?

AP Pre-Calculus is all about understanding functions and how they model real-world scenarios. This course is designed to prepare you for college-level math and beyond. We'll explore functions through modeling, graphical analysis, and numerical methods. You'll learn to manipulate equations, understand inverses, and apply transformations. The focus is on understanding the relationship between inputs (domain) and outputs (range). This approach will set you up for success in calculus and other STEM fields. 🌎

#🔊 Unit 1 Breakdown: Polynomial and Rational Functions

Unit 1 focuses on polynomial and rational functions. Let's break down what each of these entails:

#Polynomial Functions

A polynomial function is a sum of terms, each consisting of a coefficient and a variable raised to a non-negative integer power. The degree of the polynomial is the highest power of the variable.

• Form: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$

#Rational Functions

A rational function is a ratio of two polynomial functions.

• Form: $f(x) = p(x)/q(x)$, where $p(x)$ and $q(x)$ are polynomials.
• Key features include vertical asymptotes, horizontal asymptotes, and sometimes holes.

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