Functions and Modeling (College Algebra) Syllabus Study Guide

Course Overview

Introduction to Functions and Modeling

This course, "Functions and Modeling," is designed for students in business, life/health sciences, agriculture, and social sciences. It covers foundational algebraic concepts, focusing on the study and application of various types of functions and equations. The course emphasizes multiple representations (symbolic, graphical, numerical, and verbal) and the use of digital tools for graphing and modeling.

• Course Code: MATH 1483-ER10S

• Semester: Spring 2026 (8 Weeks)

• Instructor: Zach Austin

• Location: SEM Center Room 2E6 / Math Lab 2G6(B)

Course Content and Topics

Main Topics Covered

• Relations and Functions: Understanding the general concepts of relations and functions, including their definitions and representations.

• Polynomial Functions: Study of linear, quadratic, and higher-degree polynomial functions.

• Rational Functions: Analysis of functions expressed as ratios of polynomials.

• Exponential and Logarithmic Functions: Exploration of growth and decay models, and their applications.

• Equations and Inequalities: Techniques for solving various types of equations and inequalities using algebraic and digital methods.

• Systems of Equations and Matrices: Solving systems using algebraic methods and matrix operations.

• Modeling and Data Analysis: Applying algebraic techniques and digital resources to model real-life phenomena, including regression analysis.

Learning Outcomes

Key Skills and Competencies

• Interpretation of Functions: Translate between symbolic, graphical, numerical, and verbal representations of functions in real-world contexts.

• Analysis of Function Families: Identify and analyze linear, polynomial, rational, exponential, and logarithmic functions.

• Understanding Function Characteristics: Determine and interpret key features such as asymptotes, concavity, end behavior, extrema, intervals of increase/decrease, and turning points.

• Function Operations: Combine and modify functions through operations such as composition, and apply transformations. Includes applications to cost, revenue, and profit functions.

• Modeling and Problem Solving: Use algebraic and digital techniques to create, analyze, and interpret models for real-life problems, including systems of equations.

Course Materials

Required and Optional Resources

• MyMathLab Access: Online platform for assignments, tutorials, and the digital textbook. Access is provided upon enrollment.

• Calculator: Use Desmos Graphing Calculator for all graphing and calculation needs.

• Optional Textbook: College Algebra in Context: With Applications for the Managerial, Life and Social Sciences, 6th Edition, Harshbarger and Yocco (2021).

Assessment and Grading

Grading Criteria and Policies

• Homework (MyMathLab): 40% of final grade. Multiple attempts allowed until the deadline.

• Exams: 60% of final grade. In-class exams; optional retake available to replace the lowest non-misconduct grade.

Letter Grade	Percentage Range	GPA Equivalent
A	90 - 100%	4.0
B	80 - 89%	3.0
C	70 - 79%	2.0
D	60 - 69%	1.0
F	0 - 59%	0.0

• Makeup Policy: Makeup exams/quizzes allowed only with timely communication and valid reasons.

• No Dropped Exams: All exam grades count; one optional retake may replace the lowest grade (except in cases of academic misconduct).

Course Policies and Support

Attendance and Communication

• Attendance: Required from the start of the course; non-attendance may result in withdrawal and fees.

• Communication: Email is the preferred method; responses within one business day.

• Exam Return: Exams returned by the next class period.

Accommodations and Support

• Disability Accommodations: Contact the Office of Student Accessibility and Support for academic adjustments.

• Pregnancy and Parenting: Reasonable accommodations provided in accordance with Title IX.

• Title IX: Support and reporting mechanisms for sexual misconduct and related issues.

Copyright and Academic Integrity

• Copyright: Course materials are protected; do not upload to AI sites without permission.

• Academic Misconduct: Grades affected by misconduct are not eligible for replacement by retake exams.

Micro-Credential Information

Career-Related Skills Recognition

• This course may count toward a micro-credential, which recognizes specific career-related skills and competencies.

• Upon completion, students may receive a digital badge via Credly.

Summary Table: Main Function Types Covered

Function Type	General Form	Key Features
Linear	$y = mx + b$	Constant rate of change; straight line
Quadratic	$y = ax^2 + bx + c$	Parabola; vertex, axis of symmetry
Polynomial	$y = a_nx^n + \ldots + a_1x + a_0$	Multiple turning points; end behavior depends on degree
Rational	$y = \frac{p(x)}{q(x)}$	Asymptotes; undefined where $q(x) = 0$
Exponential	$y = ab^x$	Rapid growth/decay; horizontal asymptote
Logarithmic	$y = a \log_b(x) + c$	Inverse of exponential; vertical asymptote

Example: Real-World Application of Functions

• Cost Function (Business): $C(x) = 500 + 20x$ where $C(x)$ is the total cost for producing $x$ items, $500$is the fixed cost, and $20$ is the variable cost per item.

• Exponential Growth (Biology): $P(t) = P_0 e^{rt}$ models population growth, where $P_0$ is the initial population, $r$ is the growth rate, and $t$ is time.

Additional Info

• This course is not intended for STEM majors who require engineering calculus; it transfers as "Functions and Modeling," not as "Math for STEM" or traditional College Algebra.

• Students are encouraged to use digital tools for graphing and modeling throughout the course.