College Algebra (MATH-1314) Course Overview and Study Guide

Course Description

Introduction to College Algebra

College Algebra is a foundational mathematics course that explores the properties and applications of polynomial, rational, radical, exponential, and logarithmic functions. The course also covers systems of equations, matrices, and may include additional topics such as sequences, series, and probability.

• Credit Hours: 3 semester hours

• Contact Hours: 48 total

• Prerequisite: College readiness in mathematics according to TSIA standards

Course Outcomes

Learning Objectives

Upon successful completion of College Algebra, students will be able to:

1. Demonstrate and apply knowledge of functions: Understand domain and range, operations, compositions, and inverses.

2. Recognize and solve equations: Work with polynomial, rational, radical, exponential, and logarithmic functions.

3. Apply graphing techniques: Graph various types of functions and analyze their properties.

4. Evaluate roots: Find roots of higher degree polynomial and rational functions.

5. Solve systems of linear equations: Use matrices and algebraic methods to solve systems.

Key Topics in College Algebra

Functions

Functions are a central concept in algebra, representing relationships between sets of numbers.

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

• Types: Polynomial, rational, radical, exponential, and logarithmic functions.

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

• Inverse Functions: If $f(x)$ is a function, its inverse $f^{-1}(x)$ satisfies $f(f^{-1}(x)) = x$.

• Domain and Range: The set of possible inputs and outputs, respectively.

• Example: $f(x) = 2x + 3$ is a linear function with domain $(- , )$ and range $(- , )$.

Equations and Inequalities

Solving equations and inequalities is fundamental to algebraic problem-solving.

• Polynomial Equations: Equations involving terms with variables raised to whole number powers.

• Rational Equations: Equations involving ratios of polynomials.

• Radical Equations: Equations involving roots, such as square roots.

• Exponential and Logarithmic Equations: Equations involving exponential growth/decay and logarithms.

• Example: Solve $x^2 - 5x + 6 = 0$ by factoring: $(x-2)(x-3) = 0$, so $x = 2$ or $x = 3$.

Graphing Techniques

Graphing is used to visualize functions and their properties.

• Key Features: Intercepts, asymptotes, intervals of increase/decrease, maxima/minima.

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

• Example: The graph of $f(x) = x^2$ is a parabola opening upward.

Roots of Polynomial and Rational Functions

Finding roots (solutions) is essential for understanding the behavior of functions.

• Definition: A root of a function $f(x)$ is a value $x$ such that $f(x) = 0$.

• Methods: Factoring, quadratic formula, synthetic division.

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for $ax^2 + bx + c = 0$.

• Example: Find roots of $x^2 + 4x + 4 = 0$: $x = -2$ (double root).

Systems of Linear Equations and Matrices

Systems of equations are solved using algebraic and matrix methods.

• Definition: A system of equations is a set of equations with the same variables.

• Methods: Substitution, elimination, and matrix methods (such as Gaussian elimination).

• Matrix Representation: Systems can be written as $AX = B$, where $A$ is a matrix of coefficients.

• Example: Solve $\begin{cases} x + y = 5 \\ 2x - y = 4 \end{cases}$ by elimination.

Course Materials

Textbook and Online Resources

• Textbook: College Algebra (8th ed.) by Blitzer, R. (2022), Pearson.

• MyMathLab: Online homework and resources are included with the course.

• Digital Access: eBook and courseware available through campus systems.

Course Requirements

Technology and Participation

• Required Technology: Computer, microphone, external webcam, high-speed internet.

• Participation: Active engagement in lectures and online assignments is required.

• Homework: Completed through MyLab Math (MLM).

Evaluation Criteria

Grading Breakdown

Grades are determined by participation, homework, and exams. The following table summarizes the evaluation criteria:

Type	Weight	Notes
Class Participation	10%	Measured by engagement during lectures, including attentiveness and asking questions.
Homework	20%	Completed through MyLab Math; due dates available to students via MLM.
Final Exam	20%	Comprehensive; rules for calculators and notes apply.

Grade Scale

Grade	Range	Notes
A	90-100	Exceptional knowledge of the material covered
B	80-89	Above average knowledge of the material covered
C	69-79	Average knowledge of the material covered

Course Policies

Electronic Devices

• Only approved calculators may be used during exams.

• Electronic devices not approved for use are prohibited during exams.

• Up to 5 sheets of additional paper may be provided for notes if allowed by the instructor.

Attendance and Disability Services

• Attendance is required and subject to college policies.

• Students with disabilities may request accommodations through the Office of Disability Services.

Additional info:

• Topics such as sequences, series, and probability may be included depending on instructor discretion.

• Students are expected to maintain academic integrity and follow all college policies.