College Algebra (Precalculus) Syllabus and Course Overview

Course Overview

This course, College Algebra (MTH 140), is designed to prepare students for further study in mathematics, including Calculus. The curriculum covers foundational topics in algebra and functions, which are essential for success in Precalculus and beyond.

Textbook and Materials

• Textbook: A Graphical Approach to Precalculus with Limits w/MyMathLab by Hornsby, Pearson (Publisher)

• Calculator: Non-graphing scientific calculator (e.g., TI-30XS Multiview). Calculators with graphing or equation-solving capabilities are prohibited on all tests, exams, and quizzes.

Course Purpose

College Algebra fulfills the mathematics requirement for the associate of arts degree and serves as a prerequisite for Calculus. The course emphasizes problem-solving, critical thinking, and quantitative literacy.

Institutional Student Learning Outcomes (ISLOs)

• Higher Order Thinking: Distinguishing among opinions, facts, and inferences; applying evaluative standards; creative thinking; and quantitative literacy.

Course Learning Outcomes (CLOs)

Upon successful completion, students will be able to:

1. Use function notation and interpret functions in various contexts.

2. Analyze linear functions, graphs, and equations with applications.

3. Solve quadratic, polynomial, rational, and absolute value inequalities.

4. Graph basic functions and their transformations.

5. Work with absolute value and piecewise functions.

6. Perform function operations and compositions.

7. Analyze quadratic functions, graphs, and equations.

8. Analyze polynomial functions, graphs, and equations.

9. Analyze rational functions, graphs, and equations.

10. Analyze root functions, graphs, and equations.

11. Analyze power functions and equations.

12. Analyze inverse functions and graphs.

13. Analyze exponential and logarithmic functions, graphs, and equations.

14. Solve systems of equations in two and three variables with applications.

Main Topics and Subtopics

1. Linear Functions, Equations, and Inequalities

• Definition: A linear function is a function of the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• Key Properties:

  • Graph is a straight line.

  • Slope-intercept form: $y = mx + b$

  • Point-slope form: $y - y_1 = m(x - x_1)$

• Example: Find the equation of a line passing through $(2, 3)$ with slope $4$.

  • Using point-slope form: $y - 3 = 4(x - 2)$

  • Simplified: $y = 4x - 5$

2. Analysis of Graphs of Functions

• Key Concepts: Domain, range, intercepts, symmetry, transformations (shifts, stretches, reflections).

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

3. Quadratic Functions

• Standard Form: $f(x) = ax^2 + bx + c$

• Vertex Form: $f(x) = a(x - h)^2 + k$

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

• Example: Solve $x^2 - 5x + 6 = 0$.

  • Factoring: $(x - 2)(x - 3) = 0 \implies x = 2, 3$

4. Polynomial and Rational Functions

• Polynomial Function: $f(x) = a_nx^n + \ldots + a_1x + a_0$

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

• Key Concepts: End behavior, zeros, asymptotes, holes.

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

5. Exponential and Logarithmic Functions

• Exponential Function: $f(x) = a^x$, $a > 0$, $a \neq 1$

• Logarithmic Function: $f(x) = \log_a x$, inverse of exponential function

• Properties:

  • $a^{\log_a x} = x$

  • $\log_a (xy) = \log_a x + \log_a y$

  • $\log_a (x^r) = r \log_a x$

• Example: Solve $2^x = 8$.

  • $x = \log_2 8 = 3$

6. Systems of Equations

• Definition: A set of two or more equations with the same variables.

• Methods of Solution: Substitution, elimination, matrices.

• Example: Solve the system:

  • $x + y = 5$

  • $x - y = 1$

  • Add: $2x = 6 \implies x = 3$, then $y = 2$

Assignment and Grading Overview

Assignment Type	Description
Assignments	Weekly homework and practice problems
Quizzes	Short assessments on recent material
Exams	Major tests covering multiple chapters

Policies and Expectations

• Attendance: Participation in online activities is required.

• Academic Honesty: Cheating and plagiarism are strictly prohibited.

• Study Time: Expect to spend approximately 2-4 hours per week per credit hour on coursework.

• Technology: Use of Microsoft 365 and official student email is required for communication and assignments.

Additional Info

• This syllabus provides a comprehensive overview of the topics and expectations for a College Algebra course, which aligns closely with the standard Precalculus curriculum.

• For detailed weekly content and assignment due dates, refer to the course's online learning platform.