Family Overview

Pre-calculus · AP · Polynomial and Rational Functions

What this topic is

In Pre-calculus · AP, this CED topic focuses on: Rational Functions and Holes. In plain terms, students should be able to explain the main idea in their own words and complete a straightforward practice item with justification.

This topic is assessed on the AP Exam.

Why it matters

• Reading structure from polynomial/rational forms prevents later modeling mistakes.
• Polynomial and rational work is the backbone of AP Precalculus Unit 1 and later function modeling.
• Students must read end behavior, zeros, and asymptotes from equations and graphs—skills tested on MC and FRQ.
• Clear algebra on rational expressions prevents cascade errors in later units.
• Families who hear “what happens as x gets large?” are hearing exam-ready language.

How you can support

• Ask them to predict end behavior and intercepts before graphing technology.
• Ask: “What happens to the graph as x goes to positive and negative infinity?”
• Ask them to name zeros vs holes vs vertical asymptotes on one example.
• Praise a correct factor or cancel step even if arithmetic still needs fixing.
• Keep sessions short: one graph + one equation rewrite is enough.
• If a calculator graph is used, still ask what the algebra predicted first.

What not to do

• Do not cancel factors without discussing holes vs asymptotes.
• Do not treat every undefined x-value as an asymptote (holes cancel).
• Do not skip saying domain restrictions out loud.
• Do not let a pretty calculator graph replace checking end behavior algebraically.
• Do not solve every homework factoring step for them.