Math 191. College Algebra and Functions

Summer 2025

Instructor: Enrique Treviño
Lectures: two-or-three times a week on Microsoft Teams.
Office Hours: MTWF 12:00-1:00pm, and by appointment.
Office: Brown Hall 123
Email: trevino@lakeforest.edu
Phone Ext.: #6187

Announcements

Announcements for the class will be posted here.

For your convenience, here's a link to the Homework page.

Course Description

To develop a strong foundation in algebraic functions including linear, quadratic, polynomial, rational, and important transcendental functions such as exponential and logarithmic functions. The course will explore their properties, graphs, and real-world applications through multiple representations: symbolic, numerical, graphic.

Textbook

Modeling Functions and Graphs: Algebra for College Students (4th edition) by Yoshiwara.

The book is available free online, here.

Topics to be covered

The following is a tentative list of topics that will be covered:

Chapter 1: Functions and their Graphs
1.1 Linear Models
1.2 Functions
1.3 Graphs of Functions
1.5 Linear Functions

Chapter 2: Modeling with Functions
2.1 Nonlinear Models
2.2 Some Basic Functions
2.3 Transformation of Graphs
2.4 Functions as Mathematical Models
2.5 The Absolute Value Function
2.6 Domain and Range

Chapter 3: Power Functions
3.2 Integer Exponents
3.3 Roots and Radicals
3.4 Rational Exponents

Chapter 4: Exponential Functions
4.1 Exponential Growth and Decay
4.2 Exponential Functions
4.3 Logarithms
4.4 Properties of Logarithms
4.5 Exponential Models

Chapter 5: Logarithmic Functions
5.1 Inverse Functions
5.2 Logarithmic Functions
5.3 The Natural Base

Chapter 6: Quadratic Functions
6.1 Factors and x-Intercepts
6.2 Solving Quadratic Equations
6.3 Graphing Parabolas
6.5 Quadratic Inequalities

Chapter 7: Polynomial and Rational Functions
7.1 Polynomial Functions
7.2 Graphing Polynomial Functions
7.5 Equations that Include Algebraic Functions

Chapter 8: Linear Systems
8.1 Systems of Equations in Two Variables
8.2 Systems of Equations in Three Variables
8.4 Linear Inequalities

Student Learning Outcomes

Some main learning outcomes include:

Be able to do algebraic manipulations.
Be able to model problems with linear functions.
Know what a function is, how to graph it, what its graph means.
Learn exponential and logarithmic functions.
Learn how to apply the above to problems.
Learn some analytic geometry.

In general, the student should be able to understand most of the topics covered in the class and be able to use the tools to solve new problems.

Grading

The course grade will be based on:
Homework         20%
Midterm 1            20%,
Midterm 2            20%,
Final Exam          40%.

Homework

There will be regular written homework. The homework will be turned in and will reinforce the matertial learned in class. Collaboration in the homework is permitted, however you must write your own solutions in your own words (or symbols). You must also support your answers with the intermediate steps you took to reach the answer.
You can find the homework assignments for this class below:
Homework.

Exams

On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams. Also, no calculators or notes are permitted. I will provide simple calculators in the exam.
The following dates are tentative dates for the exams:

The first midterm will be on Tuesday June 3.

The second midterm will be on Tuesday June 17.

The final exam will be a cumulutive three hour exam. It will be on Friday June 27.

Attendance

Students are expected to attend every lecture and every exam. If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

Description of instructional time and expectations:

This course meets two to three times per week for 3.0 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours). This course is 6-weeks long course, therefore sudents are expected to devote a minimum of 30 hours of total work per week (in-class time plus out-of-class work) to this course.

Academic Honesty

Please read the College's information on Academic Honesty. If a student cheats in an exam, quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.

Academic Resources, Protocols, and Policies

Click here: Academic Resources, Protocols, and Policies

Last modified on May 23, 2025.