Course Overview

Introduction to College Algebra

College Algebra (MAC 1105) is a foundational mathematics course designed to develop students' problem-solving skills, critical thinking, and computational proficiency. The course covers a wide range of algebraic concepts, focusing on equations, functions, and their graphs, with an emphasis on quadratic, exponential, and logarithmic functions. Students will learn to solve equations and inequalities, understand the properties of functions, and apply mathematical modeling to real-world situations.

Course Learning Outcomes

State Learning Outcomes

• Solve equations and inequalities using appropriate techniques.

• Define and describe functions, their properties, and graphs.

• Manipulate functions to simplify expressions and find new functions.

• Use transformations to write equations for functions and graph them.

• Model and solve real-world problems using functions.

Institution Learning Outcomes

• Solve equations and inequalities.

• Interpret function notation and perform operations on functions.

• Analyze algebraic functions and their graphs.

• Analyze exponential and logarithmic functions.

• Apply mathematical modeling to real-world situations.

• Solve systems of equations and inequalities.

Course Outline

1. Equations and Inequalities

This section reviews linear equations, formulas, literal equations, and inequalities. It also covers absolute value equations, quadratic equations (including complex solutions), rational equations, and radical equations.

• Linear Equations in One Variable

• Formulas and Literal Equations

• Linear and Compound Inequalities

• Applications of Linear Equations and Inequalities

• Absolute Value Equations and Inequalities

• Quadratic Equations: Factoring, Principle of Square Roots, Completing the Square, Quadratic Formula

• Equations Reducible to Quadratic Form

• Rational and Radical Equations

2. Relations and Functions

Students will learn about relations, functions, domain and range, function notation, and operations on functions. The section also covers composite and inverse functions, properties of graphs, and symmetry.

• Definition of Relations and Functions

• Domain and Range

• Circles in Center-Radius and General Form

• Function Notation and Evaluation

• Operations on Functions: Addition, Subtraction, Multiplication, Division, Composition

• Difference Quotient

• Inverse Functions: Definition, Notation, One-to-One, Finding Formulas, Graphs

• Properties of Graphs: Intercepts, Symmetry, Even/Odd/Neither, Increasing/Decreasing/Constant, Relative Extrema

3. Analysis of Functions and Their Graphs

This section focuses on the graphical analysis of linear, quadratic, polynomial, rational, and piece-wise defined functions. It includes transformations of basic functions and modeling applications.

• Graphs of Linear Equations and Slope

• Graphs of Quadratic Functions: Vertex, Intercepts, Axis of Symmetry

• Graphs of Polynomial Functions: Degree, Leading Coefficient, End Behavior, Roots, Multiplicity

• Graphs of Rational Functions: Domain, Asymptotes, Intercepts

• Piece-wise Defined Functions: Evaluation and Graphs

• Transformations: Absolute Value, Quadratic, Square Root, Cubic, Cube Root, Reciprocal, Exponential, Logarithmic

4. Exponential and Logarithmic Functions

Students will explore the properties of exponents, logarithms, and their applications. The section includes converting between exponential and logarithmic forms, solving related equations, and modeling real-world phenomena.

• Properties of Exponents

• Definition of Logarithms: Common, Natural, Other Bases

• Change of Base Formula

• Converting Between Exponential and Logarithmic Forms

• Properties of Logarithms

• Exponential and Logarithmic Equations

• Graphs: Domain, Range, Asymptotes

• Applications: Growth and Decay, Half-life, Doubling Time, Compound Interest, Newton’s Law of Cooling, Orders of Magnitude

5. Systems of Equations and Inequalities

This section covers solving systems of linear and non-linear equations and inequalities, including applications and optional topics on three-variable systems.

• Systems of Two Equations in Two Unknowns: Linear and Non-linear

• Systems of Three Equations in Three Unknowns (Optional)

• Systems of Inequalities: Linear and Non-linear

Grading Policy

Letter grades are assigned as follows:

Additional grade details include the possibility of an 'Incomplete' (I) grade under specific circumstances.

Course Logistics and Support

• Instructor: Leo Ocean

• Email: leo.ocean@fscj.edu

• Office Hours: Monday - Wednesday, 6:00 - 7:35 PM

• Location: Classroom, SOUTH BLDG G ROOM 0302

• Required Materials: Digital courseware via FSCJ ACCESS program

• Session Length: 12 Weeks

• Important Dates: Class starts Sep 21, 2026; Refund deadline Sep 28, 2026; Withdraw deadline Nov 12, 2026; Class ends Dec 15, 2026

Policies and Resources

• Attendance: Regular attendance is expected.

• Late Work: Late work is generally not accepted; contact instructor for extensions.

• Academic Honesty: Cheating, plagiarism, and other forms of dishonesty are prohibited.

• Accessibility: Accommodations are available for students with disabilities.

• Support Services: Library, tutoring, and technology support are available to all students.

Technology Requirements

• Reliable computer or laptop with internet connectivity

• Access to necessary software applications

• Stable internet connection

• FSCJ student email for communication

• Access to Canvas Learning Management System

Additional Information

For further details, students should consult the FSCJ Support Hub, IT Services Site, Student Handbook, and other college resources. The instructor reserves the right to modify the syllabus as needed.