Course Overview

Introduction to College Algebra

This course, Math 1200-01, is designed to provide students with a comprehensive understanding of algebraic concepts, function modeling, and real-world applications. The curriculum emphasizes conceptual understanding, computational skills, and data analysis using various types of functions.

• Course Format: Face-to-face instruction with scheduled meetings.

• Required Text: College Algebra with Modeling and Visualization (6th Edition, Pearson, 2019) by Gary K. Rockswold et al.

• Learning Platforms: Pearson MyLab Math (MyMathLab) and Brightspace.

• Co-requisite: MATH 1195 for students not placed in MATH 1200.

Course Objectives and Learning Outcomes

General Education Outcomes

The course supports university-wide outcomes, including communication, critical thinking, inquiry, and understanding the interaction between science, technology, and society.

• Effective Communication: Demonstrate oral and written skills through exams, homework, reflections, and quizzes.

• Critical Thinking: Apply analytical reasoning and problem-solving skills.

• Inquiry: Use basic vocabularies and methods from various disciplines.

• Science and Society: Understand the relationship between mathematics, technology, and the environment.

Course-Specific Objectives

• Function Notation: Understand and apply function notation.

• Exponential and Logarithmic Functions: Analyze algebraic and graphical properties.

• Modeling: Fit linear, quadratic, logarithmic, and exponential models to data.

• Transformations: Understand translations, reflections, symmetries, compressions, and stretches of functions.

• Polynomials and Rational Functions: Analyze algebraic and graphical properties.

Student Learning Outcomes

• Translate word problems into mathematical equations or inequalities.

• Solve linear equalities and inequalities in one variable.

• Perform arithmetic with complex numbers.

• Solve quadratic equations by factoring or using the quadratic formula.

• Write equations of lines given points or slope.

• Sketch graphs of lines from equations.

• Solve systems of two linear equations in two variables.

• Evaluate functions for various values of x.

• Find implied domains for functions.

• Analyze graphs for increasing/decreasing behavior and concavity.

• Graph basic functions and use transformations.

• Evaluate piecewise-defined functions.

• Calculate and express function compositions.

• Graph rational functions and determine asymptotes.

• Find inverses of one-to-one functions.

• Graph and solve exponential and logarithmic functions and equations.

• Solve compound interest problems using exponentials and logarithms.

Course Structure and Assessment

Assessment Methods

• Exams: Four exams, calculator allowed, scheduled dates.

• Quizzes: Regular quizzes via MyMathLab.

• Homework: Assigned and submitted through MyMathLab.

• Reflections: Written assignments via Brightspace to support mathematical communication.

• Participation: Active engagement in class activities and discussions.

Grading Criteria

Grades are determined by weighted averages of exams, quizzes, homework, participation, and reflections. No exam scores are dropped. Partial credit may be awarded.

Note: The exact grade cutoffs (A, B, C, D, F) are referenced by images in the original file and are not specified here.

Course Calendar and Topics

Weekly Schedule Overview

The course follows a structured weekly schedule, covering key topics in College Algebra. Homework and quizzes are due weekly, and exams are scheduled throughout the semester.

All homework assignments are due by 11:59 PM Sunday each week.

Key College Algebra Topics

Functions and Their Representation

Functions are fundamental objects in algebra, representing relationships between input and output values. Understanding function notation and graphical representation is essential for modeling real-world phenomena.

• Definition: A function f is a rule that assigns to each element x in a domain exactly one element y in a range.

• Notation: denotes the value of the function at x.

• Example: is a linear function.

Types of Functions and Their Rates of Change

Different types of functions (linear, quadratic, polynomial, exponential, logarithmic) exhibit distinct behaviors and rates of change. Understanding these helps in modeling and solving real-world problems.

• Linear Function:

• Quadratic Function:

• Exponential Function:

• Logarithmic Function:

• Rate of Change: For linear functions, the rate of change is constant; for nonlinear functions, it varies.

Modeling with Functions

Modeling involves using functions to represent and analyze real-world data. This includes fitting data to appropriate function types and interpreting the results.

• Example: Modeling population growth with an exponential function.

• Equation:

Transformations of Graphs

Transformations modify the appearance of function graphs, including translations, reflections, stretches, and compressions.

• Translation: shifts the graph horizontally by h and vertically by k.

• Reflection: reflects across the x-axis.

• Stretch/Compression: stretches if and compresses if .

Polynomial and Rational Functions

Polynomial functions are sums of powers of x with coefficients, while rational functions are ratios of polynomials.

• Polynomial Function:

• Rational Function: where

• Asymptotes: Rational functions may have vertical and horizontal asymptotes.

Exponential and Logarithmic Functions

Exponential functions model rapid growth or decay, while logarithmic functions are their inverses and model processes like sound intensity or pH.

• Exponential Function:

• Logarithmic Function:

• Properties: and

• Example: Compound interest:

Solving Equations and Inequalities

Solving equations and inequalities is a core skill in algebra, including linear, quadratic, exponential, and logarithmic types.

• Quadratic Formula:

• Solving Exponential Equations: Use logarithms to isolate the variable.

• Solving Logarithmic Equations: Use exponentiation to isolate the variable.

Course Policies and Support

Attendance and Participation

Regular attendance and active participation are required. Students must engage in class activities, discussions, and complete assignments by deadlines.

Academic Integrity and AI Usage

AI tools may be used for learning support but not for submitting solutions. Academic misconduct includes plagiarism, cheating, and non-original work.

Support Resources

• Learning Assistant: Available for course-related questions and study sessions.

• Tutoring: Contact the Learning Assistance Center for individualized support.

Accessibility and Accommodations

Students with disabilities should contact the Abilities Office for accommodations. Emergency procedures and university policies are outlined in the syllabus addenda.

Summary Table: Major College Algebra Topics

Additional info:

• Grade cutoffs (A, B, C, D, F) are referenced by images and not specified in the text.

• Course calendar is tentative and subject to change.

• All major College Algebra topics are covered, aligning with standard curriculum.