AP®︎ Precalculus Unit 1: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 1 of AP Precalculus – Polynomial and Rational Functions.
Unit 1: Polynomial and Rational Functions
This unit develops understanding of polynomial and rational functions by analyzing their behavior, key features like asymptotes and end behavior, and how they can model relationships between changing quantities.
Begin with Topic 1.1: Change in TandemTo review Unit 1, go through each of the 14 topics below.
Everything you actually need to know for your Unit 1 test, pulled directly from the AP® Precalculus curriculum.
Change in Tandem
Change in Tandem
- What a Function Is
- How Input and Output Vary Together
- Concavity and Rate of Change
Rates of Change
Rates of Change
- What Rates of Change Mean
- Finding Average Rate of Change from Any Representation
- Approximating Rate of Change at a Point
Rates of Change in Linear and Quadratic Functions
Rates of Change in Linear and Quadratic Functions
- Average rate of change
- Rate patterns for linear and quadratic functions
- How to find and compare rates
Polynomial Functions and Rates of Change
Polynomial Functions and Rates of Change
- What Polynomial Functions Are
- Increasing, Decreasing, and Extrema
- Real Zeros and the Required Extremum Between Them
Polynomial Functions and Complex Zeros
Polynomial Functions and Complex Zeros
- What Polynomial Zeros Tell You
- Zeros, Multiplicity, and Complex Conjugates
- Finding and Using Zeros
Polynomial Functions and End Behavior
Polynomial Functions and End Behavior
- What End Behavior Is
- The Leading Term Controls the Ends
- Finding End Behavior from an Equation
Rational Functions and End Behavior
Rational Functions and End Behavior
- What Rational Function End Behavior Is
- The Three Degree Cases
- When the Graph Has Slant or Polynomial End Behavior
Rational Functions and Zeros
Rational Functions and Zeros
- What Zeros of a Rational Function Are
- Finding Zeros Analytically
- Zeros from Graphs, Tables, and Technology
Rational Functions and Vertical Asymptotes
Rational Functions and Vertical Asymptotes
- What Vertical Asymptotes Are
- Which Denominator Zeros Become Vertical Asymptotes
- How to Find Vertical Asymptotes from an Equation
Rational Functions and Holes
Rational Functions and Holes
- What a Hole Is
- How Common Factors Create Holes
- Finding the Coordinates of a Hole
Equivalent Representations of Polynomial and Rational Expressions
Equivalent Representations of Polynomial and Rational Expressions
- What Equivalent Forms Show
- Reading Polynomials and Rational Expressions from the Right Form
- Polynomial Long Division and Asymptotes
Transformations of Functions
Transformations of Functions
- What Function Transformations Do
- The Four Basic Transformations
- Building and Reading Combined Transformations
Function Model Selection and Assumption Articulation
Function Model Selection and Assumption Articulation
- Choosing a Function Model
- Evidence for Each Function Type
- Finite Differences and Point-Based Clues
Function Model Construction and Application
Function Model Construction and Application
- What a Complete Function Model Is
- Building the Model from Conditions or Structure
- Building the Model with Transformations, Regression, and Pieces
Notes
1 credit used · 5/5 remaining