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Module 1: Introduction to Functions & The Coordinate Plane

Welcome to College Algebra! In this module, you'll explore the foundation of algebra: real numbers, the coordinate plane, functions, and transformations.

4 Lessons
~2-3 hours
15 Practice Problems
Module Quiz

Your Progress

Pre-Assessment
Lessons 1-4
Practice
Module Quiz
Post-Assessment

Learning Objectives

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

  • Classify real numbers and plot points on the Cartesian coordinate plane
  • Calculate distance and midpoint between two points using formulas
  • Distinguish between relations and functions using multiple representations
  • Evaluate functions using function notation and determine domain and range
  • Perform function arithmetic (addition, subtraction, multiplication, division)
  • Graph parent functions and apply transformations (shifts, stretches, reflections)

Why This Matters

Functions are the language of mathematics and science! Every formula you'll use in calculus, physics, economics, and computer science is built on the foundation of functions.

This module gives you the essential skills to:

  • Understand relationships between variables in science and economics
  • Model real-world situations mathematically
  • Succeed in calculus and higher-level STEM courses
  • Develop problem-solving skills valued in all careers
  • Build confidence in your mathematical abilities

Get Started: Pre-Assessment

Before You Begin...

Take a quick 5-question pre-assessment to see what you already know. This isn't graded and won't affect your score—it's just to help us (and you!) understand your starting point.

Why do this? At the end of the module, you'll retake the same assessment and see how much you've learned. Students love seeing their progress!

Start Pre-Assessment (5 min) Skip to Lessons

Recommended: Take the pre-assessment! It only takes 5 minutes and helps you track your learning.

Module Lessons

1

Real Numbers & The Coordinate Plane

Learn the real number system hierarchy, plot points on the Cartesian plane, and use the distance and midpoint formulas.

25-30 minutes

Start Lesson 1
2

Relations & Introduction to Functions

Discover what makes a relation a function, apply the vertical line test, use function notation, and find domain and range.

30-35 minutes

Start Lesson 2
3

Function Arithmetic

Learn to add, subtract, multiply, and divide functions. Master finding domains of combined functions, including division restrictions.

25-30 minutes

Start Lesson 3
4

Graphs of Functions & Transformations

Master the 6 parent functions and learn to apply transformations: shifts, stretches, compressions, and reflections.

35-40 minutes

Start Lesson 4

After the Lessons

Practice Problems

Apply what you've learned with 15 practice problems covering all module topics. Step-by-step solutions included!

Practice Problems

Module Quiz

Test your understanding with a 12-question quiz. Pass with 70% (9 correct) to earn your Module 1 badge!

Take Module Quiz

Study Materials

Download printable study guides and quick reference cards. Perfect for exam prep!

Study Guide Quick Ref Card

Interactive Visualizations

Explore interactive graphs of parent functions, transformations, and the coordinate plane throughout the lessons!

Tips for Success

  • Practice, practice, practice - Algebra is a skill that improves with repetition. Do the problems!
  • Master the basics first - Understanding parent functions makes transformations much easier.
  • Draw graphs - Visualizing functions helps you understand them deeply.
  • Watch for tricky signs - Horizontal shifts are opposite of the sign: f(x-3) shifts RIGHT!
  • Check your domain - Always consider restrictions like division by zero and square roots of negatives.
  • Don't fear mistakes - Every mathematician makes errors. Learn from them and keep going!
Begin Module 1 →