College Algebra Syllabus and Course Structure – Study Guide

Course Overview

This study guide summarizes the structure, expectations, and main content areas of a College Algebra course (MAC 1105) as outlined in the provided syllabus. The course is designed to develop algebraic skills and concepts essential for further study in mathematics, science, engineering, business, and technology.

Course Structure and Policies

Instructional Methodologies

• Mode of Instruction: Online via MyMathLab (Pearson platform).

• Materials: MyMathLab access code, scientific calculator (required), graphing calculator (recommended), access to a computer.

• Textbook: College Algebra Essentials by Robert Blitzer (6th or 7th edition recommended).

• Supplemental Resources: PowerPoint slides, videos, and online practice available within MyMathLab.

Grading Policy

• Tests (65%): Five tests (including the final exam); lowest test score dropped.

• Online Quizzes (20%): Eight quizzes; lowest quiz score dropped.

• Online Homework (15%): Multiple attempts allowed; practice problems available but not graded.

• Grade Scale:

  • A: 90–100%

  • B: 80–89%

  • C: 70–79%

  • D: 60–69%

  • F: Below 60% or Academic Dishonesty

Course Policies

• Attendance: No scheduled meetings; students must submit all work by deadlines.

• Academic Integrity: Cheating, plagiarism, or dishonesty results in an F for the course.

• Accommodations: Available through the Office of Services for Students with Disabilities.

• Tutoring: Free tutoring available on campus and online (e.g., Khan Academy, YouTube).

Course Content and Objectives

The course covers the following main topics, each with specific learning objectives:

1. Functions and Graphs

• Relations and Functions: Definition, identification, and distinction between relations and functions.

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

• Function Notation: Using and interpreting notation such as $f(x)$.

• Difference Quotient: Evaluating and simplifying the expression $\frac{f(x+h)-f(x)}{h}$.

• Linear Functions: Identifying, graphing, and solving applied problems.

• Operations with Functions: Addition, subtraction, multiplication, division, and composition of functions.

• Graph Characteristics: Symmetry, extrema (maximum and minimum points), and intervals of increase/decrease.

• Graphing Basic and Piecewise Functions: Plotting standard and piecewise-defined functions.

• Graphical Transformations: Shifts, reflections, stretches, and compressions.

• Inverse Functions: Finding and graphing inverses algebraically and graphically.

2. Polynomial Functions

• Quadratic Functions: Graphing and solving optimization problems.

• Polynomial Graphs: Analyzing end behavior and multiplicity of zeros.

• Polynomial Inequalities: Solving and interpreting solutions.

3. Rational Functions

• Graphing Rational Functions: Identifying intercepts, vertical/horizontal asymptotes, and end behavior.

• Rational Inequalities: Solving and applying to real-world problems.

• Applications: Modeling and solving problems involving rational functions.

4. Exponential and Logarithmic Functions

• Exponential and Logarithmic Forms: Converting between forms, e.g., $y = b^x$ and $x = \log_b y$.

• Evaluating Expressions: Calculating values of exponential and logarithmic expressions.

• Properties of Logarithms: Applying properties such as $\log_b(xy) = \log_b x + \log_b y$.

• Change of Base Formula: $\log_b a = \frac{\log_c a}{\log_c b}$.

• Graphing: Plotting exponential and logarithmic functions.

• Equations: Solving exponential and logarithmic equations.

• Applications: Exponential growth and decay problems.

5. Systems of Equations and Inequalities

• Linear Systems in Three Variables: Solving using elimination or substitution.

• Nonlinear Systems: Solving systems involving nonlinear equations in two variables.

• Systems of Inequalities: Graphical solutions and interpretation.

• Applications: Modeling and solving real-world problems using systems.

Sample Schedule of Topics and Assignments

The course follows a structured schedule, with homework, quizzes, and tests assigned to specific sections. Students are expected to complete assignments in the order listed and adhere to all deadlines.

Suggested Homework Assignments

Practice problems are recommended from each chapter to reinforce learning. For example:

• Chapter 1: Sections 1.5, 1.6, 1.7 – Problems on equations, inequalities, and applications.

• Chapter 2: Sections 2.1–2.7 – Problems on functions, graphs, and transformations.

• Chapter 3: Sections 3.1, 3.2, 3.5, 3.6 – Problems on polynomial and rational functions.

• Chapter 4: Sections 4.1–4.5 – Problems on exponential and logarithmic functions.

• Chapter 5: Sections 5.2, 5.4, 5.5 – Problems on systems of equations and inequalities.

Course Success Tips

• Read each textbook section before attempting homework.

• Keep an organized notebook with sections for the syllabus, quizzes, and homework.

• Plan to spend at least 8 hours per week on coursework.

• Do not wait until the last day to complete assignments or quizzes.

• Seek help early from the instructor or tutoring resources if needed.

Table: Main Course Topics and Associated Chapters

Main Topic	Chapter(s)	Key Concepts
Prerequisites & Fundamental Concepts	Ch. P	Basic algebraic operations, properties of real numbers
Equations and Inequalities	Ch. 1	Linear, quadratic, absolute value equations and inequalities
Functions and Graphs	Ch. 2	Function notation, domain/range, transformations, inverses
Polynomial and Rational Functions	Ch. 3	Graphing, zeros, asymptotes, inequalities
Exponential and Logarithmic Functions	Ch. 4	Properties, equations, applications
Systems of Equations and Inequalities	Ch. 5	Linear/nonlinear systems, graphical solutions

Example: Evaluating a Difference Quotient

Given $f(x) = x^2 + 3x$, evaluate the difference quotient $\frac{f(x+h)-f(x)}{h}$.

• Step 1: Compute $f(x+h) = (x+h)^2 + 3(x+h) = x^2 + 2xh + h^2 + 3x + 3h$

• Step 2: Compute $f(x+h) - f(x) = [x^2 + 2xh + h^2 + 3x + 3h] - [x^2 + 3x] = 2xh + h^2 + 3h$

• Step 3: Divide by $h$: $\frac{2xh + h^2 + 3h}{h} = 2x + h + 3$

Additional Info

• Students are encouraged to use online resources and seek help as needed.

• All assignments, quizzes, and tests are administered through MyMathLab; Canvas is used for communication only.

• Late work is not accepted under any circumstances.