Unit 3 — Polynomial, Radical & Rational Functions

Unit 3 · Polynomial, Radical & Rational Functions

Polynomial, Radical & Rational Functions

Analyze a rich family of functions — from complex numbers and quadratics to higher-degree polynomials, rational expressions, radical functions, and variation models.

Estimated Time

5–6 weeks

Difficulty

Advanced

9 Lessons
9 Learning Goals
20 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 3 — Polynomial, Radical & Rational Functions is the most algebraically demanding unit of the course. It begins with complex numbers and quadratics, then moves to higher-degree polynomials — end behavior, zeros, and division. You will then graph rational functions using asymptotes and holes, explore radical functions and their inverse relationships, and close with variation models that appear throughout physics, chemistry, and economics.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Define a function and identify functions from tables, graphs, and mapping diagrams.
Goal 2Use the vertical line test to determine whether a graph represents a function.
Goal 3Read and write function notation f(x) and evaluate functions for given input values.
Goal 4Identify the domain (inputs) and range (outputs) of a function.
Goal 5Graph linear functions using slope and y-intercept in slope-intercept form y = mx + b.
Goal 6Calculate slope as rate of change between two points and interpret its meaning in context.

Skills You Will Master

Identifying functions
Function notation f(x)
Domain & range
Graphing linear functions
Slope & rate of change
Real-world applications

Real-World Connection

Functions are everywhere. When a streaming service recommends a show based on your watch history, it is using a function. When a GPS calculates your arrival time based on distance and speed, that is a function. Businesses use functions to model revenue, scientists use them to track population growth, and engineers use them to design bridges. Understanding functions — and especially linear functions — gives you the mathematical lens to describe, predict, and analyze the world around you.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter