MAT 151 College Algebra/Functions – Syllabus and Study Guide

Course Overview

Course Title and Description

MAT 151: College Algebra/Functions is a foundational mathematics course designed for college students. The course focuses on the analysis and interpretation of the behavior and nature of functions, including linear, quadratic, higher-order polynomial, rational, exponential, logarithmic, power, absolute value, and piecewise-defined functions. Students will also study systems of equations, modeling, and solving real-world problems using mathematical techniques.

• Credits: 4

• Prerequisites: Grade of C or better in MAT090, MAT095, MAT096, MAT114, MAT115, or MAT12+, or appropriate placement, or permission of Department/Division Chair.

Course Competencies

Key Learning Outcomes

• Average Rate of Change: Calculate and interpret the average rate of change in various contexts using function notation, including the difference quotient.

• Relations and Functions: Define, distinguish, and interpret relations and functions and their inverses, represented verbally, graphically, numerically, or algebraically.

• Function Evaluation and Equations: Evaluate functions, including composition, and solve function equations and inequalities using multiple methods, including matrices where appropriate.

• Function Types and Transformations: Identify, graph, analyze, and determine the key characteristics of the following function types and their transformations: linear, quadratic, higher-order polynomial, power, radical, rational, exponential, logarithmic, absolute value, and piecewise-defined.

• Mathematical Modeling: Model real-world situations using a variety of mathematical techniques (including regression) and solve real-world mathematical problems using functions.

Required Materials and Technologies

Textbook

• Title: Algebra & Trigonometry

• Subtitle: With Interactive Assignments

• Author: Kirk Trigsted

• Publisher: Pearson

• Edition: 4e

• ISBN: 978-0-13-8602789

Software and Tools

• MyMathLab (MML): Required for online assignments and assessments.

• Google Chrome: Recommended browser for accessing course materials.

• District Email: Official communication channel.

• Scanning App: Required for uploading handwritten work (e.g., Adobe Scan).

• Calculator: Use Desmos.com for calculations and graphs.

Grading Standards & Practice

Grading Scale

Letter Grade	Percent Range	Point Span
A	89.5-100%	895-1000
B	79.5-89.4%	795-894
C	69.5-79.4%	695-794
D	59.5-69.4%	595-694
F	0-59.4%	0-594

You will receive a grade of F if you earn less than 594 points or fail to complete the course by the established date, or without benefit of an official withdrawal.

Course Design and Assessment

• Online Assignments: 100 points

• 6 Module Assessments: 25 points each (150 points total)

• 6 Free Response Reviews: 25 points each (150 points total)

• In-Person Midterm: 300 points

• In-Person Final Exam: 300 points

• Total: 1000 points

Course Policies

Attendance Requirements

• Active participation is required each week. Logging in alone does not count as attendance.

• Examples of academic activity: submitting assignments, taking exams/quizzes, attending study groups, or contacting faculty about course content.

• Failure to participate for 7 consecutive days may result in withdrawal from the course.

Withdrawal Policy

• Students may withdraw at any time with a "W" grade by emailing the instructor.

• Inactivity for more than 7 days will prompt a warning email; failure to respond within 48 hours will result in withdrawal.

• Withdrawal can affect financial aid and scholarships.

Assignment and Assessment Policies

• Online Assignments: Completed in MyMathLab, graded on accuracy. Late work receives a penalty.

• Module Assessments: Six assessments, each with a three-day window. Must be completed in one sitting.

• Free Response Reviews: Handwritten, scanned, and uploaded to Canvas. Must be legible and organized.

• Midterm and Final: In-person, proctored exams required for all students.

Key Mathematical Concepts

Functions and Their Properties

• Definition: A function is a relation in which each input (domain) has exactly one output (range).

• Notation: $f(x)$ denotes the value of function $f$ at input $x$.

• Types of Functions: Linear, quadratic, polynomial, rational, exponential, logarithmic, absolute value, piecewise-defined.

• Inverse Functions: If $f(g(x)) = x$ and $g(f(x)) = x$, then $g$ is the inverse of $f$.

Average Rate of Change

• Definition: The average rate of change of a function $f$ over the interval $[a, b]$ is:

$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

Difference Quotient

• Definition: The difference quotient is used to compute the average rate of change over a small interval:

$\frac{f(x+h) - f(x)}{h}$

Solving Equations and Inequalities

• Techniques include factoring, using the quadratic formula, graphing, and applying properties of exponents and logarithms.

• Systems of equations can be solved by substitution, elimination, or using matrices.

Transformations of Functions

• Shifts, reflections, stretches, and compressions can be applied to parent functions to obtain new functions.

• Example: $f(x) = (x-2)^2 + 3$ is a shift of the parent quadratic function $y = x^2$ right by 2 units and up by 3 units.

Modeling and Applications

• Functions are used to model real-world phenomena such as population growth (exponential), depreciation (linear), and projectile motion (quadratic).

• Regression techniques can be used to fit functions to data.

Course Technology and Communication

• All students must use their district-provided email for official communication.

• Assignments and assessments are submitted via Canvas and MyMathLab.

• Google Chrome is the recommended browser.

• Desmos.com is used for graphing and calculations.

Summary Table: Types of Functions and Key Properties

Function Type	General Form	Key Features
Linear	$f(x) = mx + b$	Constant rate of change, straight line graph
Quadratic	$f(x) = ax^2 + bx + c$	Parabola, vertex, axis of symmetry
Polynomial	$f(x) = a_nx^n + \ldots + a_0$	Degree, end behavior, turning points
Rational	$f(x) = \frac{p(x)}{q(x)}$	Asymptotes, holes, domain restrictions
Exponential	$f(x) = ab^x$	Growth/decay, horizontal asymptote
Logarithmic	$f(x) = a \log_b(x) + c$	Inverse of exponential, vertical asymptote
Absolute Value	$f(x) = a|x-h| + k$	V-shape, vertex at $(h, k)$
Piecewise	Defined by cases	Different rules for different intervals

Additional info:

• This syllabus provides a comprehensive overview of the course structure, expectations, and key mathematical concepts for College Algebra/Functions (MAT 151).

• Students are expected to engage with both online and in-person components, including proctored exams.

• Mastery of function concepts and mathematical modeling is essential for success in this course and for further study in mathematics.