College Algebra Course Outline and Study Guide

Course Outline: College Algebra (MATH 1314-113/613)

Overview

This course covers foundational and advanced topics in College Algebra, structured to build students' understanding of functions, equations, and mathematical models. The syllabus outlines the weekly progression of topics, assignments, quizzes, and exams.

Course Topics and Weekly Breakdown

Week 1: Introduction to Graphing and Functions

• 1.1 Introduction to Graphing: Basics of the Cartesian plane, plotting points, and interpreting graphs.

• 1.2 Functions and Graphs: Definition of a function, domain and range, and how to graph functions.

• 1.3 Linear Functions, Slope, and Applications: Understanding linear equations, calculating slope, and real-world applications.

Week 2: Linear Equations and Piecewise Functions

• 1.4 Equations of Lines: Forms of linear equations (point-slope, slope-intercept, standard form).

• 1.5 Linear Equations, Functions, Zeros, Applications: Solving linear equations, finding zeros, and applying concepts to problems.

• 2.1 Increasing, Decreasing, and Piecewise Functions: Identifying intervals where functions increase or decrease; introduction to piecewise-defined functions.

Week 3: Algebra and Composition of Functions

• 2.2 The Algebra of Functions: Operations with functions (addition, subtraction, multiplication, division).

• 2.3 The Composition of Functions: Combining functions using composition; notation and evaluation.

• 2.5 Transformations: Shifts, reflections, stretches, and compressions of function graphs.

Week 4: Exam 1 Review

• Comprehensive review of Chapters 1 & 2.

Week 5-6: Quadratic and Polynomial Functions

• 3.2 Quadratic Equations, Functions, Zeros, Models: Standard form, vertex, axis of symmetry, solving quadratics, and modeling with quadratics.

• 3.3 Analyzing Graphs of Quadratic Functions: Graphing quadratics, identifying key features.

• 4.1 Polynomial Functions: Introduction to higher-degree polynomials and their properties.

Week 7: Graphing and Theorems for Polynomials

• 4.2 Graphing Polynomial Functions: End behavior, turning points, and sketching graphs.

• 4.3 Remainder and Factor Theorem: Using theorems to factor and evaluate polynomials.

Week 8: Rational and Inverse Functions

• 4.5 Rational Functions: Graphs, asymptotes, and discontinuities.

• 5.1 Inverse Functions: Definition, finding inverses, and their properties.

Week 9: Exam 2 Review

• Comprehensive review of Chapters 3 & 4.

Week 10-11: Exponential and Logarithmic Functions

• 5.2 Exponential Functions and Graphs: Properties, applications, and graphing exponentials.

• 5.3 Logarithmic Functions and Graphs: Definition, properties, and graphing logarithms.

• 5.4 Properties of Logarithmic Functions: Laws of logarithms and their applications.

• 5.5 Solving Exponential and Logarithmic Equations: Techniques for solving equations involving exponents and logs.

Week 12: Applications and Systems of Equations

• 5.6 Applications: Real-world problems involving exponential and logarithmic functions.

• 6.1 Systems of Equations in Two Variables: Methods for solving systems (substitution, elimination, graphing).

Week 13: Exam 3 Review

• Comprehensive review of Chapter 5.

Week 14: Systems in Three Variables and Matrices

• 6.2 Systems of Equations in Three Variables: Extending methods to three-variable systems.

• 6.3 Matrices and Systems of Equations: Introduction to matrices, matrix operations, and using matrices to solve systems.

Week 15-16: Final Exam Review and Assessment

• Comprehensive review for the final exam covering all course material.

• Final Exam administered in Week 16.

Key Concepts and Skills

• Graphing: Understanding and interpreting various types of graphs.

• Functions: Definitions, operations, transformations, and compositions.

• Equations: Linear, quadratic, polynomial, rational, exponential, and logarithmic equations.

• Systems of Equations: Solving using algebraic and matrix methods.

• Applications: Applying algebraic concepts to real-world scenarios.

Important Dates

• Census Day: September 1, 2026

• W-Day (Withdrawal Deadline): November 13, 2026

• Final Exam: November 30, 2026

Additional info: This outline aligns with standard College Algebra curricula, covering all major topics listed in the reference chapter titles. Students are expected to complete weekly assignments, quizzes, and exams as scheduled.