Course Overview

Introduction to Precalculus Algebra

This course, MATH 1200 - Precalculus Algebra, is designed for students with a strong background in algebra. It covers fundamental concepts essential for further study in mathematics, including equations, inequalities, functions, graphs, polynomials, rational, exponential, and logarithmic functions, as well as analytic geometry. The course prepares students for calculus and other advanced mathematical subjects.

• Credit Hours: 3.0

• Prerequisite: MyMathTest Challenge Exam Level 3 score of 70 or higher or MATH 1040

• Required Text: Sullivan, Michael. Precalculus, 12th Edition (Pearson MyLab Math)

Course Objectives and Learning Outcomes

Key Skills and Knowledge Areas

Upon successful completion of this course, students will be able to:

• Identify properties, laws, and definitions of algebra.

• Factor and find real zeros of polynomials.

• Solve and graph linear and quadratic equations and inequalities; graph conic sections.

• Find the domain, range, and inverse of functions; graph functions including composite functions.

• Solve, apply, and graph exponential and logarithmic functions.

Topic Outline

Major Chapters Covered

The following chapters are included in the course, each focusing on a fundamental area of precalculus:

• Chapter 1: Graphs

• Chapter 2: Functions and Their Graphs

• Chapter 3: Linear and Quadratic Functions

• Chapter 4: Polynomial and Rational Functions

• Chapter 5: Exponential and Logarithmic Functions

• Chapter 10: Analytic Geometry

Expanded Chapter Summaries

Chapter 1: Graphs

This chapter introduces the concept of graphs as visual representations of mathematical relationships. Students learn to plot points, interpret graphs, and understand the connection between equations and their graphical forms.

• Key Concepts: Cartesian coordinate system, plotting points, interpreting graphs

• Example: Plotting the graph of

Chapter 2: Functions and Their Graphs

Functions are central to precalculus. This chapter explores the definition of a function, domain and range, and how to graph various types of functions.

• Definition: A function is a relation in which each input has exactly one output.

• Domain and Range: The set of possible input values (domain) and output values (range).

• Example: The function has domain and range .

Chapter 3: Linear and Quadratic Functions

This chapter covers linear and quadratic functions, their properties, and their graphs. Students learn to solve equations and inequalities involving these functions.

• Linear Function:

• Quadratic Function:

• Example: Solving yields and .

Chapter 4: Polynomial and Rational Functions

Students study higher-degree polynomials and rational functions, including factoring, finding zeros, and graphing.

• Polynomial Function:

• Rational Function: where

• Example: Factoring

Chapter 5: Exponential and Logarithmic Functions

This chapter introduces exponential and logarithmic functions, their properties, and applications.

• Exponential Function:

• Logarithmic Function:

• Example: Solving gives .

Chapter 10: Analytic Geometry

Analytic geometry explores the properties and graphs of conic sections, including circles, parabolas, ellipses, and hyperbolas.

• Conic Sections: Circle, parabola, ellipse, hyperbola

• Example: The equation of a circle:

Assessment and Grading

Evaluation Methods

Student performance is assessed through quizzes, homework, midterm, and final exams. The grading scale is based on weighted averages of these components.

Grading Scale

Additional Academic Resources

Support Services

Students are encouraged to utilize university resources such as the Tutoring and Testing Center, Writing and Communications Center, and the Center for Student Counseling and Well-Being for academic and personal support.

Summary

This syllabus provides a comprehensive overview of the precalculus algebra course, including its objectives, major topics, assessment methods, and available resources. Students should refer to the official textbook and MyLab Math for detailed content and practice problems.