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

Course Overview

Introduction to College Algebra

College Algebra (MATH-1314) is a foundational mathematics course designed to develop students' understanding of algebraic concepts, functions, and problem-solving skills. The course covers a range of topics including polynomial, rational, exponential, and logarithmic functions, as well as systems of equations and matrices.

• Course Credits: 3

• Prerequisites: Completion of TSI Algebraic Math requirements or equivalent coursework.

• Instructor: Professor T. Slider

• Contact: [e-mail] | Office: W212 | Phone: [phone]

State-Defined Learning Outcomes

Core Competencies in College Algebra

Students are expected to demonstrate and apply knowledge of algebraic functions, including their domains, ranges, operations, and properties. The course emphasizes the following learning outcomes:

• Properties of Functions: Understanding domain, range, operations, and composition of functions.

• Polynomial and Rational Functions: Recognizing and applying properties, graphing techniques, and evaluating roots.

• Exponential and Logarithmic Functions: Analyzing and solving equations involving these functions.

• Systems of Linear Equations: Solving and analyzing systems using matrices.

Texas Core Objectives

General Education Skills Developed

The course is designed to foster essential academic skills that support student success in college and beyond. These objectives include:

• Critical Thinking Skills: Innovation, inquiry, analysis, evaluation, and synthesis of information.

• Communication Skills: Effective development, interpretation, and expression of ideas through written, oral, and visual communication.

• Empirical and Quantitative Skills: Manipulation and analysis of numerical data or observable facts resulting in informed conclusions.

• Teamwork: Ability to consider different points of view and work effectively with others.

• Personal Responsibility: Ability to connect choices, actions, and consequences to ethical decision-making.

• Social Responsibility: Intercultural competence and knowledge of civic responsibility.

Graded Work

Assessment and Evaluation

Your final grade in College Algebra is determined by performance on quizzes, tests, homework, and a final exam. Assignments are completed in MyLab Math and accessed via eCampus/Brightspace.

Assignments	Percentages
Quizzes	Quiz Average × 10%
Tests	Test Average × 60%
Homework	Homework Average × 20%
Final Exam	Final Exam × 10%
TOTAL	100%

Grade Breakdown

Grade	Range	Notes
A	90-100	Excellent
B	80-89	Good
C	70-79	Average
D	60-69	Passing but not transferable
F	0-59	Failure

Course Schedule

Topics and Due Dates

The course schedule includes a summary of topics and due dates. All study materials, assignments, and tests are posted in the Pearson Course Materials tab under MyLab Math All Assignments by the end of the first week of classes.

• Unit 1: Chapters 1 & 2 due by 11:59 pm of September 26, 2025.

• Additional units and assignments will be posted as the course progresses.

Course Policies

Responsibility of Online Learner

Students are responsible for having reliable internet access and a computer to complete assignments and exams. Technical issues not related to the course platform are not considered valid excuses for late or missing work.

Student Code of Conduct / Behavior

Respectful behavior is required in all interactions. Disruptive or offensive conduct may result in removal from the online system and further disciplinary action.

Attendance and Participation

Regular participation is required. For online courses, students should log in at least five times per week and spend a minimum of nine hours per week on course activities.

• Attendance is mandatory for certification and financial aid eligibility.

• Participation includes reading, watching lectures, completing homework, and engaging in discussions.

Late Work Policy

Late work is accepted until the final submission deadline of December 6, 2025, with a 20% penalty. No assignments can be submitted after the final exam deadline.

Support Contacts

Academic Support Resources

• Success Coach: Personalized support for academic planning and graduation milestones.

• Free Tutoring: Available to all current Dallas College students for College Algebra and other subjects.

Key Mathematical Topics in College Algebra

Functions and Their Properties

Functions are a central concept in algebra, representing relationships between sets of numbers. Understanding their properties is essential for solving equations and modeling real-world scenarios.

• Definition: A function is a relation that assigns exactly one output to each input.

• Domain and Range: The domain is the set of possible inputs; the range is the set of possible outputs.

• Operations: Functions can be added, subtracted, multiplied, divided, and composed.

• Example: If $f(x) = 2x + 3$ and $g(x) = x^2$, then $(f + g)(x) = f(x) + g(x) = 2x + 3 + x^2$.

Polynomial and Rational Functions

Polynomial functions involve expressions with variables raised to whole number powers. Rational functions are ratios of polynomials.

• Polynomial Function: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ext{...} + a_1x + a_0$

• Rational Function: $f(x) = \frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x) \neq 0$

• Roots: Solutions to $f(x) = 0$ are called roots or zeros.

• Example: $f(x) = x^2 - 4$ has roots at $x = 2$ and $x = -2$.

Exponential and Logarithmic Functions

Exponential functions model growth and decay, while logarithmic functions are their inverses.

• Exponential Function: $f(x) = a^x$, where $a > 0$ and $a \neq 1$

• Logarithmic Function: $f(x) = \log_a(x)$, the inverse of $f(x) = a^x$

• Example: $f(x) = 2^x$ and $g(x) = \log_2(x)$

Systems of Equations and Matrices

Systems of equations involve finding values that satisfy multiple equations simultaneously. Matrices are used to organize and solve these systems efficiently.

• System of Linear Equations: A set of equations of the form $a_1x + b_1y = c_1$, $a_2x + b_2y = c_2$

• Matrix Representation: $\begin{bmatrix} a_1 & b_1 \\ a_2 & b_2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} c_1 \\ c_2 \end{bmatrix}$

• Example: Solve $2x + 3y = 5$ and $x - y = 2$ using matrices.

Additional info:

• Some topics such as sequences, series, probability, and conics may be included depending on the instructor's syllabus.

• Students are encouraged to use graphing technology for assignments and problem-solving.