College Algebra Syllabus and Study Guide

Course Overview

Introduction to College Algebra

This syllabus outlines the structure, expectations, and content of College Algebra (MATH 1111-120) for Fall 2025. The course provides an in-depth study of algebraic, exponential, and logarithmic functions, with emphasis on solving problems using algebraic and graphical techniques.

• Instructor: Richard Puscas

• Credit Hours: 3.0

• Prerequisite: Appropriate score on the math placement test

• Required Materials: TI-83 or TI-84 calculator, iCollege access

Course Content and Structure

Main Topics

• Unit I: Equations & Inequalities

• Unit II: Functions & Graphs

• Unit III: Polynomial & Rational Functions

• Unit IV: Exponential & Logarithmic Functions

Core Learning Outcomes

Upon completion, students will be able to:

• Apply mathematical and computational knowledge to interpret, evaluate, and communicate quantitative information using verbal, numerical, graphical, or symbolic forms.

• Demonstrate information literacy, inquiry and analysis, and problem-solving skills.

Content Standards

Functions and Their Properties

Students will understand and apply the following concepts:

• Definition of a Function: 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).

• Intervals of Increase/Decrease/Constant: Identify where a function rises, falls, or remains unchanged.

• Transformations: Vertical and horizontal shifts, stretching/compressing, and reflections.

• End Behavior: Analyze how functions behave as inputs become very large or very small.

• Asymptotes: Lines that a graph approaches but never touches.

Algebraic and Graphical Solutions

• Composition of Functions: Combining two functions to form a new function.

• Inverse Functions: Functions that reverse the effect of the original function.

• Solving Equations: Use algebraic and graphical methods to find solutions.

Types of Functions

• Linear Functions: $f(x) = mx + b$

• Quadratic Functions: $f(x) = ax^2 + bx + c$

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

• Rational Functions: $f(x) = \frac{P(x)}{Q(x)}$ where $Q(x) \neq 0$

• Exponential Functions: $f(x) = a^x$

• Logarithmic Functions: $f(x) = \log_a(x)$

Equations and Inequalities

• Solving Linear and Quadratic Equations: Use factoring, quadratic formula, and graphing.

• Solving Polynomial Equations: Factorable polynomials of degree greater than 2.

• Solving Rational Equations: Set denominators not equal to zero, find common denominators.

• Solving Exponential and Logarithmic Equations: Use properties of exponents and logarithms.

• Solving Systems of Equations: Use graphing, substitution, elimination, and matrices.

Graphing Techniques

• Graph functions and analyze their properties.

• Identify intercepts, asymptotes, and intervals of increase/decrease.

• Use technology to estimate turning points and solve equations graphically.

Grading and Policies

Grade Calculation

Component	Weight
Homework	15%
Tests	60%
Final Exam	25%

Grading Scale

Grade	Percentage
A	90–100%
B	80–89.99%
C	70–79.99%
D	60–69.99%
F	0–59.99%

Important Policies

• No Show Policy: Students not attending during the first two weeks will be dropped.

• Administrative Withdrawal: Students may be withdrawn for non-attendance during the first five weeks.

• Withdrawal Policy: Last day to withdraw is October 24, 2025. A maximum of three withdrawals allowed.

• Limited Attempts: Course may be attempted a maximum of two times.

• Academic Integrity: Cheating and plagiarism are strictly prohibited.

• Student Accommodation: Accommodations available for students with disabilities.

• Campus Carry Policy: Licensed individuals may carry handguns as per state law.

Support and Resources

• Math Lab: Free tutoring available at the Learning Resources Center (LRC-3200).

• Textbook: College Algebra (8th ed.) by Robert Blitzer, accessible through iCollege.

• Online Resources: iCollege, MyLab Math, instructor's WebEx link.

Example: Solving a Quadratic Equation

• Given: $ax^2 + bx + c = 0$

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Application: Use the formula to find the roots of any quadratic equation.

Additional Info

• Course emphasizes both algebraic and graphical approaches to problem solving.

• Technology (graphing calculators, online platforms) is integrated into assignments and exams.