Course Overview

This study guide summarizes the key topics, learning objectives, and academic expectations for Precalculus Mathematics I (MATH 134B/SMAT 121B) at Southern University A & M College. The course is designed to prepare students for further study in mathematics, focusing on foundational concepts in algebra and functions, with applications in business, science, and engineering.

Course Description and Scope

• Topics Covered: Real numbers and their properties, complex numbers, equations and inequalities, polynomial, rational, exponential, and logarithmic functions and their graphs, systems of equations and inequalities, and mathematical modeling.

• Applications: Emphasis on modeling and real-world applications.

• Technology: Use of graphing calculators and online resources (MyLabsMath, Canvas).

Course Learning Objectives

• Apply multiple strategies to solve equations and inequalities algebraically and graphically.

• Identify and analyze functions, relations, equations, and graphs.

• Evaluate and model with various types of functions: piecewise, linear, quadratic, polynomial, rational, exponential, and logarithmic.

• Find slopes and equations of lines, including parallel and perpendicular lines.

• Calculate distance, midpoint, and characteristics of circles.

• Solve applied problems involving quadratic and rational functions.

• Apply the Factor and Remainder Theorems.

• Simplify and convert logarithmic and exponential expressions.

• Solve linear systems of equations.

Course Content by Chapter

Chapter 1: Equations and Inequalities

• 1.1 Graphs and Graphing Utilities: Introduction to coordinate systems and graphing techniques.

• 1.2 Linear and Rational Equations: Methods for solving equations, including those with fractions and variables in denominators.

• 1.3 Models and Applications: Using equations to model real-world scenarios.

• 1.4 Complex Numbers: Definition, arithmetic, and applications of complex numbers.

• 1.5 Quadratic Equations: Solving by factoring, square roots, completing the square, and the quadratic formula.

• 1.6 Other Types of Equations: Techniques for solving higher-degree and special equations.

• 1.7 Linear and Absolute Value Inequalities: Solving and graphing inequalities, including those involving absolute values.

Chapter 2: Functions and Graphs

• 2.1 Basics of Functions and Their Graphs: Definition of functions, domain, range, and function notation.

• 2.2 More on Functions and Their Graphs: Analysis of function behavior and transformations.

• 2.3 Linear Functions and Slope: Slope formula, interpretation, and applications.

• 2.4 More on Slope: Parallel and perpendicular lines.

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

• 2.6 Combinations and Composite Functions: Operations with functions and composition.

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

• 2.8 Distance and Midpoint Formulas; Circles: Calculating distance and midpoint between points; standard equation of a circle.

Chapter 3: Polynomial and Rational Functions

• 3.1 Quadratic Functions: Graphing and analyzing quadratic functions.

• 3.2 Polynomial Functions and Their Graphs: Characteristics and behavior of polynomial functions.

• 3.3 Dividing Polynomials; Remainder and Factor Theorems: Polynomial division and theorems for finding zeros.

• 3.4 Zeros of Polynomial Functions: Techniques for finding and interpreting zeros.

• 3.5 Rational Functions and Their Graphs: Analysis and graphing of rational functions.

• 3.6 Polynomial and Rational Inequalities: Solving and interpreting inequalities involving polynomials and rational expressions.

Chapter 4: Exponential and Logarithmic Functions

• 4.1 Exponential Functions: Definition, properties, and applications.

• 4.2 Logarithmic Functions: Definition, properties, and relationship to exponentials.

• 4.3 Properties of Logarithms: Laws of logarithms and simplification techniques.

• 4.4 Exponential and Logarithmic Equations: Methods for solving equations involving exponentials and logarithms.

• 4.5 Exponential Growth and Decay; Modeling Data: Applications in real-world contexts, such as population growth and radioactive decay.

Chapter 8: Systems of Equations and Inequalities

• 8.1 Systems of Linear Equations in Two Variables: Methods for solving systems (substitution, elimination, graphical), and applications.

Key Definitions and Formulas

• Linear Equation: An equation of the form .

• Quadratic Equation: An equation of the form .

• Quadratic Formula:

• Slope Formula:

• Distance Formula:

• Midpoint Formula:

• Standard Form of a Circle:

• Exponential Function:

• Logarithmic Function:

• Properties of Logarithms:

Sample Table: Grading Scale

Academic Expectations and Policies

• Assignments: All work must be submitted on time, with clear, logical steps and correct mathematical notation.

• Participation: Active engagement in discussions and online activities is required.

• Technology: Use of Canvas, MyLabsMath, and other university resources is mandatory.

• Academic Integrity: Plagiarism and academic dishonesty are strictly prohibited.

• Accessibility: Accommodations are available for students with documented disabilities.

Program Learning Outcomes

• Solve mathematical problems using appropriate strategies.

• Express mathematical concepts effectively in oral and written form.

• Engage in mathematical modeling of real-world phenomena.

• Use technology to aid in problem-solving.

• Demonstrate understanding of mathematical proof and logical reasoning.

Additional Info

• This syllabus provides a comprehensive overview of the course structure, expectations, and core mathematical content. For detailed lesson plans, assignments, and resources, refer to the Canvas course site and the required textbook: Algebra and Trigonometry, 8th Edition, Robert Blitzer.