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MATH 115: College Algebra

A study of algebraic equations, inequalities, graphs, and functions — including linear, quadratic, absolute value, rational, radical, polynomial, exponential, and logarithmic functions. Prerequisite: ACT Math 21 or higher, SAT Math 530 or higher, or MATH 108 with a "C" or higher.

Current Sections Fall 2026

115-04W Online Asynchronous · Syllabus & materials

General Information

Office Location and Office Hours: Science Hall 202A — MW 11:00 AM – 1:00 PM, F 11:00 AM – 12:00 PM, or by appointment.

Lecture Notes by Topic

Lecture notes with worked solutions — opens as a PDF.

Quizzes and module exams are listed for pacing — they don't link anywhere.

Module 1

Notes 1.1 Functions and Function Notation (Ch. 3.1) PDF ↗ Video How to Tell If a Graph Is a Function Shorts ↗ Video How to Read a Function Table Shorts ↗ Video Solving a Falling Object Problem in 30 Seconds Shorts ↗ Notes 1.2 Domain and Range, Interval Notation (Ch. 3.1 & 3.2) PDF ↗ Video Finding the Domain: A Fraction AND a Square Root Shorts ↗ Video How to Read Domain & Range from Function's Graph Shorts ↗ Notes 1.3 Linear Functions (Ch. 4.1) PDF ↗ Video Linear Growth of Population in a City: A Real-World Example Shorts ↗ Video Two Slope-Intercept Problems in Under 30 Seconds Shorts ↗ Quiz Module 1 Quiz 1 (Lessons 1–3) Notes 1.4 Solving Systems of Linear Equations in Two Variables (Ch. 8.1) PDF ↗ Video Solving Systems by Substitution Shorts ↗ Video Elimination Method and When a System Has NO Solution Shorts ↗ Notes 1.5 Linear Inequalities (Ch. 1.5) PDF ↗ Video Solving an Inequality With Fractions (And Flip the Sign!) Shorts ↗ Video Solving a Double Inequality in One Shot Shorts ↗ Video A Real-World Inequality Problem Shorts ↗ Quiz Module 1 Quiz 2 (Lessons 4–5) Notes 1.6 Absolute Value Equations and Inequalities (Ch. 1.6) PDF ↗ Video Absolute Value Inequalities Always Do This Shorts ↗ Exam Exam 1

Module 2

Notes 2.1 Complex Numbers (Ch. 1.3) PDF ↗ Video Multiplying Complex Numbers — FOIL Still Works Shorts ↗ Video Dividing Complex Numbers — The Conjugate Trick Shorts ↗ Notes 2.2 Quadratic Equations (Ch. 1.2 & 1.3) PDF ↗ Video 3x² + 7x − 8 = 0 by Completing the Square Shorts ↗ Video When the Quadratic Formula Gives Imaginary Answers Shorts ↗ Quiz Module 2 Quiz 1 (Lessons 1–2) Notes 2.3 Quadratic Functions and Their Graphs (Ch. 4.3) PDF ↗ Video x² + 10x + 22 → Vertex Form Shorts ↗ Video Optimization: Maximizing Area With a Parabola Shorts ↗ Notes 2.4 Function Composition (Ch. 3.1 & 6.1) PDF ↗ Video f(g(x)) vs g(f(x)) — Order Matters Shorts ↗ Quiz Module 2 Quiz 2 (Lessons 3–4) Notes 2.5 Transformation of Graphs (Ch. 3.5) PDF ↗ Video Reading Transformations Straight From the Formula and Sketching the Graph Shorts ↗ Video Shift, Shift, Reflect: Transforming √x with Three Transformations Shorts ↗ Exam Exam 2

Module 3

Notes 3.1 Introduction to Polynomial Functions (Ch. 5.1) PDF ↗ Video Why Do Some Zeros Cross and Others Bounce? Two Polynomials, Two Answers Shorts ↗ Notes 3.2 Graphs of Polynomial Functions (Ch. 5.2) PDF ↗ Video Sketch Any Polynomial in 5 Steps Shorts ↗ Video Can You Reverse a Degree 4 Polynomial Straight Off Its Graph? Shorts ↗ Notes 3.3 Rational Functions and Their Graphs (Ch. 5.3 & 5.4) PDF ↗ Notes 3.3 Graphing Rational Functions PDF ↗ Video This Rational Function Is Hiding a Hole (Plus Vertical & Horizontal Asymptotes) Shorts ↗ Video Full Rational Function Graph, Every Asymptote, Every Intercept — Start to Finish Shorts ↗ Video Can a Graph Cross Its Own Asymptote? (The Rule Everyone Gets Wrong) Shorts ↗ Video Don't Miss the Hole in This Rational Function Shorts ↗ Quiz Module 3 Quiz 1 (Lessons 1–3) Notes 3.4 Radical Equations (Ch. 1.4) PDF ↗ Video Why You Always Have to Check Radical Equation Answers Shorts ↗ Video Two Square Roots, One Equation, Two Valid Answers Shorts ↗ Notes 3.5 Inverse Functions (Ch. 6.2) PDF ↗ Video How to Verify Two Functions Are Inverses Shorts ↗ Video Finding the Inverse of a Rational Function in 3 Steps — Swap, Solve, Done Shorts ↗ Quiz Module 3 Quiz 2 (Lessons 4–5) Exam Exam 3

Module 4

Notes 4.1 Exponential Functions and Their Graphs (Ch. 6.3) PDF ↗ Video Transforming an Exponential Graph Fast Shorts ↗ Video Car Depreciation: When Does It Hit $15K? Shorts ↗ Video Find the Exponential Function from Two Points Shorts ↗ Notes 4.2 Logarithmic Functions and Their Graphs (Ch. 6.4) PDF ↗ Video Graphing a Logarithmic Function with Shifts Shorts ↗ Quiz Module 4 Quiz 1 (Lessons 1–2) Notes 4.3 Logarithmic Properties (Ch. 6.5) PDF ↗ Video Careful! You Can't Split a SUM Inside a Log — Expanding Logarithms Shorts ↗ Video Combining Logs Into One — Two Examples Shorts ↗ Notes 4.4 Exponential Equations (Ch. 6.6) PDF ↗ Video Two Exponential Equations, Two Different Tricks Shorts ↗ Notes 4.4 Logarithmic Equations (Ch. 6.6) PDF ↗ Video This Log Equation Has a Sneaky Rejected Answer — Solving 2ln x − ln 5 = ln(x+10) Shorts ↗ Video How to Compute log₅(33) on Any Calculator Shorts ↗ Quiz Module 4 Quiz 2 (Lessons 3–4) Exam Final Exam

Past Semesters Complete Record

Spring 2025 (115-02, TR 11:00 AM – 12:15 PM)
Spring 2024 (115-05, TR 9:30 – 10:45 AM)