College Algebra Syllabus and Core Concepts Study Guide

Course Overview

Introduction to College Algebra

This course provides a comprehensive study of algebraic expressions, equations, inequalities, functions, and their applications. Students will develop skills in problem-solving, graphing, and mathematical reasoning, preparing them for further study in mathematics and related fields.

• Instructor: Dr. Zachacewski S. Quenette

• Required Text: Algebra, 8th edition by Blitzer, R. (Pearson, 2022)

• Prerequisite: Exit or exemption from Learning Support mathematics

• Calculator: TI-84 or equivalent

Course Structure and Grading

Assessment Components

Student performance is evaluated through tests, quizzes, homework assignments, and a comprehensive final exam. The grading breakdown is as follows:

Component	Weight (%)
Tests (3 total)	100 (each)
Quizzes (at least 4)	Probably important dates
MyMathLab Home Assignment (MML)	100
Comprehensive Final Exam	200

Course Grades:

Score (%)	Grade
90-100	A
80-89	B
70-79	C
60-69	D
Below 60	F

Major Topics and Learning Outcomes

Linear Equations and Inequalities

Students will learn to solve, graph, and interpret linear equations and inequalities in one and two variables.

• Definition: A linear equation is an equation of the form $ax + b = 0$.

• Key Properties: Solutions can be found by isolating the variable.

• Example: Solve $2x + 3 = 7$; $x = 2$.

Quadratic Equations

Quadratic equations are equations of the form $ax^2 + bx + c = 0$. Students will learn to solve these by factoring, completing the square, and using the quadratic formula.

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

• Graphing: The graph of a quadratic equation is a parabola.

• Example: Solve $x^2 - 5x + 6 = 0$; $x = 2$ or $x = 3$.

Functions and Their Graphs

Students will study the concept of a function, domain and range, and how to graph various types of functions.

• Definition: A function is a relation where each input has exactly one output.

• Function Notation: $f(x)$

• Domain and Range: The set of possible inputs (domain) and outputs (range).

• Example: For $f(x) = x^2$, domain is all real numbers, range is $[0, \infty)$.

Polynomial and Rational Functions

Students will analyze polynomial and rational functions, including their graphs, zeros, and asymptotic behavior.

• Polynomial Function: $f(x) = ax^n + bx^{n-1} + ... + k$

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

• Asymptotes: Vertical and horizontal asymptotes describe the behavior of rational functions.

• Example: $f(x) = \frac{1}{x-2}$ has a vertical asymptote at $x=2$.

Exponential and Logarithmic Functions

Students will study the properties, graphs, and applications of exponential and logarithmic functions.

• Exponential Function: $f(x) = a^x$

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

• Inverse Relationship: Exponential and logarithmic functions are inverses.

• Example: $\log_2 8 = 3$ because $2^3 = 8$.

Systems of Equations

Students will solve systems of linear equations using substitution, elimination, and graphical methods.

• System of Equations: Two or more equations with multiple variables.

• Solution Methods: Substitution, elimination, graphing.

• Example: Solve $x + y = 5$ and $x - y = 1$; $x = 3$, $y = 2$.

Modeling and Applications

Students will apply algebraic concepts to model real-world scenarios, including growth and decay, and data analysis.

• Growth and Decay: Exponential models describe population growth and radioactive decay.

• Data Modeling: Use equations to fit data and make predictions.

• Example: $P(t) = P_0 e^{rt}$ models exponential growth.

Graph Transformations

Students will learn to perform vertical and horizontal shifts, stretches, compressions, and reflections on graphs of functions.

• Vertical Shift: $f(x) + k$ shifts the graph up by $k$ units.

• Horizontal Shift: $f(x + h)$ shifts the graph left by $h$ units.

• Reflection: $-f(x)$ reflects the graph across the x-axis.

• Example: $f(x) = (x-2)^2 + 3$ is a parabola shifted right by 2 and up by 3.

Inverse Functions

Students will identify and compute inverse functions, understanding domain and range restrictions.

• Inverse Function: $f^{-1}(x)$ reverses the effect of $f(x)$.

• Finding Inverses: Swap $x$ and $y$ and solve for $y$.

• Example: If $f(x) = 2x + 3$, then $f^{-1}(x) = \frac{x-3}{2}$.

Circles and Distance in the Plane

Students will find the equation of a circle and calculate distances between points in the coordinate plane.

• Circle Equation: $(x-h)^2 + (y-k)^2 = r^2$

• Distance Formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

• Example: Find the equation of a circle with center $(2,3)$ and radius $5$:$(x-2)^2 + (y-3)^2 = 25$.

Academic Policies and Integrity

Expectations

Students are expected to attend all classes, complete assignments on time, and adhere to the university's academic integrity policies. Cheating, plagiarism, and other forms of academic dishonesty are strictly prohibited.

• Attendance: Required for success; excessive absences may result in grade penalties.

• Make-up Policy: Students must provide documentation for missed exams or assignments.

• Academic Integrity: All work must be original; collaboration is allowed only when specified.

Course Schedule (Sample)

Date	Section	Homework
M 8/25	1.2 - Syllabus and Linear Equations and Rational Equations	1-40, 71-76
W 8/27	1.7 - Linear Inequalities	24-76
M 9/1	2.4 - Quadratic Equations	1-36, 65, 88, 134,135,143
W 9/3	Test 1
M 9/8	3.2 - Linear Functions and Slope	51-88, 459, 87-88
W 9/10	3.3 - Rate of Change	1-31, 459, 50-100, 101-104
M 9/15	3.4 - Transformations of Functions	1-31, 459, 50-100, 101-104
W 9/17	Test 2
M 9/22	4.1 - Polynomial Functions and Their Graphs	1-31, 459, 50-100, 101-104
W 9/24	4.2 - Rational Functions and Their Graphs	5-20, 22-32, 45-56, 459
M 9/29	5.1 - Exponential Functions	1-31, 459, 50-100, 101-104
W 10/1	5.2 - Logarithmic Functions	1-31, 459, 50-100, 101-104
M 10/6	Test 3
W 12/10	Final Exam	11:30am – 2:00pm (Arrive 20 mins early)

Additional info:

• Some details about specific homework assignments and dates were inferred from the schedule table.

• Key learning outcomes and standards for each function type were expanded for clarity.