College Algebra: Course Overview and Key Concepts

College Algebra: Course Overview and Key Concepts

Course Description and Objectives

This course provides an introduction to elementary functions and graphing for mathematics, science, business, and engineering majors. It prepares students for calculus by covering polynomial, rational, exponential, and logarithmic functions, as well as their applications.

• Emphasis: Function notation, graphing, and mathematical modeling.

• Applications: Real-world problems in mathematics, science, business, and engineering.

Prerequisites

• ACT Composite Math score of 23 or better, or equivalent placement exam score.

• Completion of MATH 0930 or equivalent with a grade of C or better.

Extended Course Description

The course is designed to help students gain mathematical knowledge and skills using algebra concepts to solve problems. It includes:

• Use of function notation and graphing techniques.

• Solving equations and inequalities.

• Applications involving polynomial, rational, exponential, and logarithmic functions.

• Use of graphing calculators and technology for problem-solving.

Student Learning Outcomes

Upon successful completion of the course, students will be able to:

1. Use function concepts, including graphing, transformations, composition, inverses, and translations.

2. Analyze and interpret mathematical equations and data to solve problems.

3. Model and solve real-world problems using polynomial, rational, exponential, and logarithmic functions.

4. Use technology, such as graphing calculators, to support mathematical reasoning.

Key Topics and Concepts

1. Functions and Their Properties

Functions are fundamental objects in algebra, representing relationships between variables.

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

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

• Types of Functions: Polynomial, rational, exponential, logarithmic.

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

Example: The function $f(x) = 2x + 3$ is a linear function with domain $(-\infty, \infty)$ and range $(-\infty, \infty)$.

2. Graphing Functions

Graphing is a visual way to understand the behavior of functions.

• Transformations: Shifts, stretches, compressions, and reflections of graphs.

• Intercepts: Points where the graph crosses the axes.

• Asymptotes: Lines that the graph approaches but never touches (common in rational and exponential functions).

Example: The graph of $f(x) = x^2$ is a parabola opening upwards with vertex at (0,0).

3. Solving Equations and Inequalities

Solving equations and inequalities is essential for finding unknown values and analyzing mathematical models.

• Linear Equations: $ax + b = 0$

• Quadratic Equations: $ax^2 + bx + c = 0$

• Rational Equations: Equations involving fractions with polynomials in the numerator and denominator.

• Exponential and Logarithmic Equations: $a^x = b$, $\log_a(x) = b$

Example: Solve $2x + 3 = 7$:

$2x + 3 = 7$ $2x = 4$ $x = 2$

4. Applications and Mathematical Modeling

Mathematical modeling uses algebraic functions to represent and solve real-world problems.

• Word Problems: Translating real-life situations into mathematical equations.

• Regression: Using data to find the best-fit function (linear, quadratic, etc.).

• Technology: Graphing calculators and software (e.g., MyMathLab) are used for computation and visualization.

Example: Modeling population growth with an exponential function: $P(t) = P_0 e^{rt}$

Grading and Assessment

Grades are based on exams, homework, participation, and a final exam. The following table summarizes the grading scale:

Grade	Percentage
A	90 - 100
B	80 - 89
C	70 - 79
D	60 - 69
F	Below 60

Required Materials and Technology

• Textbook: Blitzer, Pearson Education, Inc.

• Calculator: TI-84 or similar graphing calculator recommended.

• Online Resources: MyMathLab for homework and assignments.

Support and Resources

• Math Learning Center: Offers tutoring and learning materials for algebra, arithmetic, and geometry.

• Instructor Office Hours: Available for questions and additional help.

• Online Videos: Khan Academy, YouTube, and other educational platforms.

Class Policies and Schedule

• Participation in Moodle and MyLab Math is required for assignments and discussions.

• Homework and exams must be completed as scheduled.

• Withdrawal and audit policies are outlined in the syllabus and college guidelines.

Additional info: The course emphasizes the use of technology and mathematical modeling to prepare students for further studies in calculus and related fields.