AP Precalculus

What This Unit Covers Unit 1 serves as the foundation for AP Precalculus by establishing the behavior and analysis of polynomial and rational functions. Students will explore how these functions change, examine their graphical characteristics—such as zeros, asymptotes, and end behavior—and learn to construct mathematical models to represent real-world phenomena.

Why It Matters on the Exam Polynomial and Rational Functions make up approximately 20–25% of the AP Precalculus exam, making it a critical area for scoring well. You can expect a mix of multiple-choice and free-response questions that require you to interpret graphical features, analyze rates of change, and algebraically manipulate expressions to solve context-based problems.

How to Study It

• Master the End Behavior: Focus on how the degrees of the numerator and denominator in a rational function dictate horizontal asymptotes and long-run behavior.
• Practice Algebraic Manipulation: Spend time simplifying complex rational expressions and practicing polynomial division, as these skills are essential for identifying holes and vertical asymptotes.
• Focus on Context: Don't just solve for $x$; practice connecting the mathematical model to the real-world scenario (e.g., explaining what a vertical asymptote represents in a physical model).
• Use Visuals for Transformations: Create a "transformation cheat sheet" to visualize how shifting, scaling, and reflecting functions change their key features like intercepts and domain.